Haskell 2010 Language Report

Simon Marlow (editor)

Copyright notice. The authors and publisher intend this Report to belong to the entire Haskell community, and grant permission to copy and distribute it for any purpose, provided that it is reproduced in its entirety, including this Notice. Modiﬁed versions of this Report may also be copied and distributed for any purpose, provided that the modiﬁed version is clearly presented as such, and that it does not claim to be a deﬁnition of the language Haskell 2010.

“Some half dozen persons have written technically on combinatory logic, and most of these, including ourselves, have published something erroneous. Since some of our fellow sinners are among the most careful and competent logicians on the contemporary scene, we regard this as evidence that the subject is refractory. Thus fullness of exposition is necessary for accuracy; and excessive condensation would be false economy here, even more than it is ordinarily.” Haskell B. Curry and Robert Feys in the Preface to Combinatory Logic [3], May 31, 1956

In September of 1987 a meeting was held at the conference on Functional Programming Languages and Computer Architecture (FPCA ’87) in Portland, Oregon, to discuss an unfortunate situation in the functional programming community: there had come into being more than a dozen non-strict, purely functional programming languages, all similar in expressive power and semantic underpinnings. There was a strong consensus at this meeting that more widespread use of this class of functional languages was being hampered by the lack of a common language. It was decided that a committee should be formed to design such a language, providing faster communication of new ideas, a stable foundation for real applications development, and a vehicle through which others would be encouraged to use functional languages. This document describes the result of that (and subsequent) committee’s efforts: a purely functional programming language called Haskell, named after the logician Haskell B. Curry whose work provides the logical basis for much of ours.

Goals
The committee’s primary goal was to design a language that satisﬁed these constraints: 1. It should be suitable for teaching, research, and applications, including building large systems. 2. It should be completely described via the publication of a formal syntax and semantics. 3. It should be freely available. Anyone should be permitted to implement the language and distribute it to whomever they please. 4. It should be based on ideas that enjoy a wide consensus. 5. It should reduce unnecessary diversity in functional programming languages. xiii

xiv

PREFACE

Haskell 2010: language and libraries
The committee intended that Haskell would serve as a basis for future research in language design, and hoped that extensions or variants of the language would appear, incorporating experimental features. Haskell has indeed evolved continuously since its original publication. By the middle of 1997, there had been ﬁve versions of the language design (from Haskell 1.0 – 1.4). At the 1997 Haskell Workshop in Amsterdam, it was decided that a stable variant of Haskell was needed; this became “Haskell 98” and was published in February 1999. The ﬁxing of minor bugs led to the Revised Haskell 98 Report in 2002. At the 2005 Haskell Workshop, the consensus was that so many extensions to the ofﬁcial language were widely used (and supported by multiple implementations), that it was worthwhile to deﬁne another iteration of the language standard, essentially to codify (and legitimise) the status quo. The Haskell Prime effort was thus conceived as a relatively conservative extension of Haskell 98, taking on board new features only where they were well understood and widely agreed upon. It too was intended to be a “stable” language, yet reﬂecting the considerable progress in research on language design in recent years. After several years exploring the design space, it was decided that a single monolithic revision of the language was too large a task, and the best way to make progress was to evolve the language in small incremental steps, each revision integrating only a small number of well-understood extensions and changes. Haskell 2010 is the ﬁrst revision to be created in this way, and new revisions are expected once per year.

Introduction
Haskell is a general purpose, purely functional programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-deﬁned algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a rich set of primitive datatypes, including lists, arrays, arbitrary and ﬁxed precision integers, and ﬂoating-point numbers. Haskell is both the culmination and solidiﬁcation of many years of research on non-strict functional languages. This report deﬁnes the syntax for Haskell programs and an informal abstract semantics for the meaning of such programs. We leave as implementation dependent the ways in which Haskell programs are to be manipulated, interpreted, compiled, etc. This includes such issues as the nature of programming environments and the error messages returned for undeﬁned programs (i.e. programs that formally evaluate to ⊥).

1.1

Program Structure

In this section, we describe the abstract syntactic and semantic structure of Haskell, as well as how it relates to the organization of the rest of the report. 1. At the topmost level a Haskell program is a set of modules, described in Chapter 5. Modules provide a way to control namespaces and to re-use software in large programs. 2. The top level of a module consists of a collection of declarations, of which there are several kinds, all described in Chapter 4. Declarations deﬁne things such as ordinary values, datatypes, type classes, and ﬁxity information. 3. At the next lower level are expressions, described in Chapter 3. An expression denotes a value and has a static type; expressions are at the heart of Haskell programming “in the small.” 4. At the bottom level is Haskell’s lexical structure, deﬁned in Chapter 2. The lexical structure captures the concrete representation of Haskell programs in text ﬁles. This report proceeds bottom-up with respect to Haskell’s syntactic structure.

3

4

CHAPTER 1. INTRODUCTION

The chapters not mentioned above are Chapter 6, which describes the standard built-in datatypes and classes in Haskell, and Chapter 7, which discusses the I/O facility in Haskell (i.e. how Haskell programs communicate with the outside world). Also, there are several chapters describing the Prelude, the concrete syntax, literate programming, the speciﬁcation of derived instances, and pragmas supported by most Haskell compilers. Examples of Haskell program fragments in running text are given in typewriter font:
let x = 1 z = x+y in z+1

“Holes” in program fragments representing arbitrary pieces of Haskell code are written in italics, as in if e1 then e2 else e3 . Generally the italicized names are mnemonic, such as e for expressions, d for declarations, t for types, etc.

1.2

The Haskell Kernel

Haskell has adopted many of the convenient syntactic structures that have become popular in functional programming. In this Report, the meaning of such syntactic sugar is given by translation into simpler constructs. If these translations are applied exhaustively, the result is a program written in a small subset of Haskell that we call the Haskell kernel. Although the kernel is not formally speciﬁed, it is essentially a slightly sugared variant of the lambda calculus with a straightforward denotational semantics. The translation of each syntactic structure into the kernel is given as the syntax is introduced. This modular design facilitates reasoning about Haskell programs and provides useful guidelines for implementors of the language.

1.3

Values and Types

An expression evaluates to a value and has a static type. Values and types are not mixed in Haskell. However, the type system allows user-deﬁned datatypes of various sorts, and permits not only parametric polymorphism (using a traditional Hindley-Milner type structure) but also ad hoc polymorphism, or overloading (using type classes). Errors in Haskell are semantically equivalent to ⊥ (“bottom”). Technically, they are indistinguishable from nontermination, so the language includes no mechanism for detecting or acting upon errors. However, implementations will probably try to provide useful information about errors. See Section 3.1.

1.4

Namespaces

There are six kinds of names in Haskell: those for variables and constructors denote values; those for type variables, type constructors, and type classes refer to entities related to the type system; and module names refer to modules. There are two constraints on naming: 1. Names for variables and type variables are identiﬁers beginning with lowercase letters or underscore; the other four kinds of names are identiﬁers beginning with uppercase letters.

1.4. NAMESPACES 2. An identiﬁer must not be used as the name of a type constructor and a class in the same scope.

5

These are the only constraints; for example, Int may simultaneously be the name of a module, class, and constructor within a single scope.

6

CHAPTER 1. INTRODUCTION

Chapter 2

Lexical Structure
In this chapter, we describe the low-level lexical structure of Haskell. Most of the details may be skipped in a ﬁrst reading of the report.

Because the syntax in this section describes lexical syntax, all whitespace is expressed explicitly; there is no implicit space between juxtaposed symbols. BNF-like syntax is used throughout, with productions having the form: nonterm → alt1 | alt2 | . . . | altn

Care must be taken in distinguishing metalogical syntax such as | and [. . .] from concrete terminal syntax (given in typewriter font) such as | and [...], although usually the context makes the distinction clear. Haskell uses the Unicode [2] character set. However, source programs are currently biased toward the ASCII character set used in earlier versions of Haskell. This syntax depends on properties of the Unicode characters as deﬁned by the Unicode consortium. Haskell compilers are expected to make use of new versions of Unicode as they are made available.

Lexical analysis should use the “maximal munch” rule: at each point, the longest possible lexeme satisfying the lexeme production is read. So, although case is a reserved word, cases is not. Similarly, although = is reserved, == and ˜= are not. Any kind of whitespace is also a proper delimiter for lexemes. Characters not in the category ANY are not valid in Haskell programs and should result in a lexing error.

2.3

Comments

Comments are valid whitespace. An ordinary comment begins with a sequence of two or more consecutive dashes (e.g. --) and extends to the following newline. The sequence of dashes must not form part of a legal lexeme. For example, “-->” or “|--” do not begin a comment, because both of these are legal lexemes; however “--foo” does start a comment. A nested comment begins with “{-” and ends with “-}”. No legal lexeme starts with “{-”; hence, for example, “{---” starts a nested comment despite the trailing dashes. The comment itself is not lexically analysed. Instead, the ﬁrst unmatched occurrence of the string “-}” terminates the nested comment. Nested comments may be nested to any depth: any occurrence of the string “{-” within the nested comment starts a new nested comment, terminated by “-}”. Within a nested comment, each “{-” is matched by a corresponding occurrence of “-}”. In an ordinary comment, the character sequences “{-” and “-}” have no special signiﬁcance, and, in a nested comment, a sequence of dashes has no special signiﬁcance. Nested comments are also used for compiler pragmas, as explained in Chapter 12. If some code is commented out using a nested comment, then any occurrence of {- or -} within a string or within an end-of-line comment in that code will interfere with the nested comments.

An identiﬁer consists of a letter followed by zero or more letters, digits, underscores, and single quotes. Identiﬁers are lexically distinguished into two namespaces (Section 1.4): those that begin with a lower-case letter (variable identiﬁers) and those that begin with an upper-case letter (constructor identiﬁers). Identiﬁers are case sensitive: name, naMe, and Name are three distinct identiﬁers (the ﬁrst two are variable identiﬁers, the last is a constructor identiﬁer).

Operator symbols are formed from one or more symbol characters, as deﬁned above, and are lexically distinguished into two namespaces (Section 1.4): • An operator symbol starting with a colon is a constructor. • An operator symbol starting with any other character is an ordinary identiﬁer. Notice that a colon by itself, “:”, is reserved solely for use as the Haskell list constructor; this makes its treatment uniform with other parts of list syntax, such as “[]” and “[a,b]”. Other than the special syntax for preﬁx negation, all operators are inﬁx, although each inﬁx operator can be used in a section to yield partially applied operators (see Section 3.5). All of the standard inﬁx operators are just predeﬁned symbols and may be rebound. In the remainder of the report six different kinds of names will be used: varid conid tyvar tycon tycls modid (variables) (constructors) (type variables) (type constructors) (type classes) (modules)

→ → → →

varid conid conid {conid .} conid

Variables and type variables are represented by identiﬁers beginning with small letters, and the others by identiﬁers beginning with capitals; also, variables and constructors have inﬁx forms, the other four do not. Module names are a dot-separated sequence of conid s. Namespaces are also discussed in Section 1.4. A name may optionally be qualiﬁed in certain circumstances by prepending them with a module identiﬁer. This applies to variable, constructor, type constructor and type class names, but not type variables or module names. Qualiﬁed names are discussed in detail in Chapter 5. qvarid qconid qtycon qtycls qvarsym qconsym → → → → → → [modid [modid [modid [modid [modid [modid .] varid .] conid .] tycon .] tycls .] varsym .] consym

2.5. NUMERIC LITERALS

11

Since a qualiﬁed name is a lexeme, no spaces are allowed between the qualiﬁer and the name. Sample lexical analyses are shown below. This Lexes as this f.g f . g (three tokens) F.g F.g (qualiﬁed ‘g’) f.. f .. (two tokens) F.. F.. (qualiﬁed ‘.’) F. F . (two tokens) The qualiﬁer does not change the syntactic treatment of a name; for example, Prelude.+ is an inﬁx operator with the same ﬁxity as the deﬁnition of + in the Prelude (Section 4.4.2).

2.5

Numeric Literals
digit{digit} octit{octit} hexit{hexit}

decimal → octal → hexadecimal →

integer

→ | |

decimal 0o octal | 0O octal 0x hexadecimal | 0X hexadecimal

ﬂoat

→ | →

decimal . decimal [exponent] decimal exponent (e | E) [+ | -] decimal

exponent

There are two distinct kinds of numeric literals: integer and ﬂoating. Integer literals may be given in decimal (the default), octal (preﬁxed by 0o or 0O) or hexadecimal notation (preﬁxed by 0x or 0X). Floating literals are always decimal. A ﬂoating literal must contain digits both before and after the decimal point; this ensures that a decimal point cannot be mistaken for another use of the dot character. Negative numeric literals are discussed in Section 3.4. The typing of numeric literals is discussed in Section 6.4.1.

Character literals are written between single quotes, as in ’a’, and strings between double quotes, as in "Hello". Escape codes may be used in characters and strings to represent special characters. Note that a single quote ’ may be used in a string, but must be escaped in a character; similarly, a double quote " may be used in a character, but must be escaped in a string. \ must always be escaped. The category charesc also includes portable representations for the characters “alert” (\a), “backspace” (\b), “form feed” (\f), “new line” (\n), “carriage return” (\r), “horizontal tab” (\t), and “vertical tab” (\v). Escape characters for the Unicode character set, including control characters such as \ˆX, are also provided. Numeric escapes such as \137 are used to designate the character with decimal representation 137; octal (e.g. \o137) and hexadecimal (e.g. \x37) representations are also allowed. Consistent with the “maximal munch” rule, numeric escape characters in strings consist of all consecutive digits and may be of arbitrary length. Similarly, the one ambiguous ASCII escape code, "\SOH", is parsed as a string of length 1. The escape character \& is provided as a “null character” to allow strings such as "\137\&9" and "\SO\&H" to be constructed (both of length two). Thus "\&" is equivalent to "" and the character ’\&’ is disallowed. Further equivalences of characters are deﬁned in Section 6.1.2. A string may include a “gap”—two backslants enclosing white characters—which is ignored. This allows one to write long strings on more than one line by writing a backslant at the end of one line and at the start of the next. For example,
"Here is a backslant \\ as well as \137, \ \a numeric escape character, and \ˆX, a control character."

Haskell permits the omission of the braces and semicolons used in several grammar productions, by using layout to convey the same information. This allows both layout-sensitive and layout-insensitive styles of coding, which can be freely mixed within one program. Because layout is not required, Haskell programs can be straightforwardly produced by other programs. The effect of layout on the meaning of a Haskell program can be completely speciﬁed by adding braces and semicolons in places determined by the layout. The meaning of this augmented program is now layout insensitive. Informally stated, the braces and semicolons are inserted as follows. The layout (or “off-side”) rule takes effect whenever the open brace is omitted after the keyword where, let, do, or of. When this happens, the indentation of the next lexeme (whether or not on a new line) is remembered and the omitted open brace is inserted (the whitespace preceding the lexeme may include comments). For each subsequent line, if it contains only whitespace or is indented more, then the previous item is continued (nothing is inserted); if it is indented the same amount, then a new item begins (a semicolon is inserted); and if it is indented less, then the layout list ends (a close brace is inserted). If the indentation of the non-brace lexeme immediately following a where, let, do or of is less than or equal to the current indentation level, then instead of starting a layout, an empty list “{}” is inserted, and layout processing occurs for the current level (i.e. insert a semicolon or close brace). A close brace is also inserted whenever the syntactic category containing the layout list ends; that is, if an illegal lexeme is encountered at a point where a close brace would be legal, a close brace is

2.7. LAYOUT

13

inserted. The layout rule matches only those open braces that it has inserted; an explicit open brace must be matched by an explicit close brace. Within these explicit open braces, no layout processing is performed for constructs outside the braces, even if a line is indented to the left of an earlier implicit open brace. Section 10.3 gives a more precise deﬁnition of the layout rules. Given these rules, a single newline may actually terminate several layout lists. Also, these rules permit:
f x = let a = 1; b = 2 g y = exp2 in exp1

making a, b and g all part of the same layout list. As an example, Figure 2.1 shows a (somewhat contrived) module and Figure 2.2 shows the result of applying the layout rule to it. Note in particular: (a) the line beginning }};pop, where the termination of the previous line invokes three applications of the layout rule, corresponding to the depth (3) of the nested where clauses, (b) the close braces in the where clause nested within the tuple and case expression, inserted because the end of the tuple was detected, and (c) the close brace at the very end, inserted because of the column 0 indentation of the end-of-ﬁle token.

For the sake of clarity, the rest of this section will assume that expressions involving inﬁx operators have been resolved according to the ﬁxities of the operators.

3.1

Errors

Errors during expression evaluation, denoted by ⊥ (“bottom”), are indistinguishable by a Haskell program from non-termination. Since Haskell is a non-strict language, all Haskell types include ⊥. That is, a value of any type may be bound to a computation that, when demanded, results in an error. When evaluated, errors cause immediate program termination and cannot be caught by the user. The Prelude provides two functions to directly cause such errors:
error :: String -> a undefined :: a

A call to error terminates execution of the program and returns an appropriate error indication to the operating system. It should also display the string in some system-dependent manner. When undefined is used, the error message is created by the compiler. Translations of Haskell expressions use error and undefined to explicitly indicate where execution time errors may occur. The actual program behavior when an error occurs is up to the implementation. The messages passed to the error function in these translations are only suggestions; implementations may choose to display more or less information when an error occurs.

Haskell provides special syntax to support inﬁx notation. An operator is a function that can be applied using inﬁx syntax (Section 3.4), or partially applied using a section (Section 3.5). An operator is either an operator symbol, such as + or $$, or is an ordinary identiﬁer enclosed in grave accents (backquotes), such as ` `. For example, instead of writing the preﬁx application op x y, one can op write the inﬁx application x ` ` y. If no ﬁxity declaration is given for ` ` then it defaults to highest op op precedence and left associativity (see Section 4.4.2). Dually, an operator symbol can be converted to an ordinary identiﬁer by enclosing it in parentheses. For example, (+) x y is equivalent to x + y, and foldr (*) 1 xs is equivalent to foldr (\x y -> x*y) 1 xs. Special syntax is used to name some constructors for some of the built-in types, as found in the production for gcon and literal . These are described in Section 6.1. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer. Similarly, a ﬂoating point literal stands for an application of fromRational to a value of type Rational (that is, Ratio Integer).

Translation: The integer literal i is equivalent to fromInteger i , where fromInteger is a method in class Num (see Section 6.4.1). The ﬂoating point literal f is equivalent to fromRational (n Ratio.% d ), where fromRational is a method in class Fractional and Ratio.% constructs a rational from two integers, as deﬁned in the Ratio library. The integers n and d are chosen so that n/d = f .

Function application is written e1 e2 . Application associates to the left, so the parentheses may be omitted in (f x) y. Because e1 could be a data constructor, partial applications of data constructors are allowed. Lambda abstractions are written \ p1 . . . pn -> e, where the pi are patterns. An expression such as \x:xs->x is syntactically incorrect; it may legally be written as \(x:xs)->x. The set of patterns must be linear—no variable may appear more than once in the set.

The form e1 qop e2 is the inﬁx application of binary operator qop to expressions e1 and e2 . The special form -e denotes preﬁx negation, the only preﬁx operator in Haskell, and is syntax for negate (e). The binary - operator does not necessarily refer to the deﬁnition of - in the Prelude; it may be rebound by the module system. However, unary - will always refer to the negate function deﬁned in the Prelude. There is no link between the local meaning of the - operator and unary negation. Preﬁx negation has the same precedence as the inﬁx operator - deﬁned in the Prelude (see Table 4.1). Because e1-e2 parses as an inﬁx application of the binary operator -, one must write e1(-e2) for the alternative parsing. Similarly, (-) is syntax for (\ x y -> x-y), as with any inﬁx operator, and does not denote (\ x -> -x)—one must use negate for that.

Sections are written as ( op e ) or ( e op ), where op is a binary operator and e is an expression. Sections are a convenient syntax for partial application of binary operators. Syntactic precedence rules apply to sections as follows. (op e) is legal if and only if (x op e) parses in the same way as (x op (e)); and similarly for (e op). For example, (*a+b) is syntactically invalid, but (+a*b) and (*(a+b)) are valid. Because (+) is left associative, (a+b+) is syntactically correct, but (+a+b) is not; the latter may legally be written as (+(a+b)). As another example, the expression
(let n = 10 in n +)

Because - is treated specially in the grammar, (- exp) is not a section, but an application of preﬁx negation, as described in the preceding section. However, there is a subtract function deﬁned in the Prelude such that (subtract exp) is equivalent to the disallowed section. The expression (+ (- exp)) can serve the same purpose.

where op is a binary operator, e is an expression, and x is a variable that does not occur free in e.

3.6
lexp

Conditionals
→ if exp [;] then exp [;] else exp

A conditional expression has the form if e1 then e2 else e3 and returns the value of e2 if the value of e1 is True, e3 if e1 is False, and ⊥ otherwise.

20 Translation: The following identity holds: =

CHAPTER 3. EXPRESSIONS

if e1 then e2 else e3

case e1 of { True -> e2 ; False -> e3 }

where True and False are the two nullary constructors from the type Bool, as deﬁned in the Prelude. The type of e1 must be Bool; e2 and e3 must have the same type, which is also the type of the entire conditional expression.

where : and [] are constructors for lists, as deﬁned in the Prelude (see Section 6.1.3). The types of e1 through ek must all be the same (call it t), and the type of the overall expression is [t] (see Section 4.1.2). The constructor “:” is reserved solely for list construction; like [], it is considered part of the language syntax, and cannot be hidden or redeﬁned. It is a right-associative operator, with precedence level 5 (Section 4.4.2).

3.8
aexp qcon

Tuples
→ | → ( exp1 , . . . , expk ) qcon (,{,}) (k ≥ 2 )

Tuples are written (e1 , . . . , ek ), and may be of arbitrary length k ≥ 2 . The constructor for an n-tuple is denoted by (,. . . ,), where there are n − 1 commas. Thus (a,b,c) and (,,) a b c denote the same value. Standard operations on tuples are given in the Prelude (see Section 6.1.4 and Chapter 9).

3.9. UNIT EXPRESSIONS AND PARENTHESIZED EXPRESSIONS

21

Translation: (e1 , . . . , ek ) for k ≥ 2 is an instance of a k -tuple as deﬁned in the Prelude, and requires no translation. If t1 through tk are the types of e1 through ek , respectively, then the type of the resulting tuple is (t1 , . . . , tk ) (see Section 4.1.2).

3.9
aexp gcon

Unit Expressions and Parenthesized Expressions
→ | → gcon ( exp ) ()

The form (e) is simply a parenthesized expression, and is equivalent to e. The unit expression () has type () (see Section 4.1.2). It is the only member of that type apart from ⊥, and can be thought of as the “nullary tuple” (see Section 6.1.5).

where enumFrom, enumFromThen, enumFromTo, and enumFromThenTo are class methods in the class Enum as deﬁned in the Prelude (see Figure 6.1). The semantics of arithmetic sequences therefore depends entirely on the instance declaration for the type t. See Section 6.3.4 for more details of which Prelude types are in Enum and their semantics.

A list comprehension has the form [ e | q1 , . . . , qn ], n ≥ 1 , where the qi qualiﬁers are either • generators of the form p <- e, where p is a pattern (see Section 3.17) of type t and e is an expression of type [t] • local bindings that provide new deﬁnitions for use in the generated expression e or subsequent boolean guards and generators • boolean guards, which are arbitrary expressions of type Bool. Such a list comprehension returns the list of elements produced by evaluating e in the successive environments created by the nested, depth-ﬁrst evaluation of the generators in the qualiﬁer list. Binding of variables occurs according to the normal pattern matching rules (see Section 3.17), and if a match fails then that element of the list is simply skipped over. Thus:
[ x | xs <- [ [(1,2),(3,4)], [(5,4),(3,2)] ], (3,x) <- xs ]

where e ranges over expressions, p over patterns, l over list-valued expressions, b over boolean expressions, decls over declaration lists, q over qualiﬁers, and Q over sequences of qualiﬁers. ok is a fresh variable. The function concatMap, and boolean value True, are deﬁned in the Prelude. As indicated by the translation of list comprehensions, variables bound by let have fully polymorphic types while those deﬁned by <- are lambda bound and are thus monomorphic (see Section 4.5.4).

3.12
lexp

Let Expressions
→ let decls in exp

Let expressions have the general form let { d1 ; . . . ; dn } in e, and introduce a nested, lexicallyscoped, mutually-recursive list of declarations (let is often called letrec in other languages). The scope of the declarations is the expression e and the right hand side of the declarations. Declarations are described in Chapter 4. Pattern bindings are matched lazily; an implicit ˜ makes these patterns irrefutable. For example,

3.13. CASE EXPRESSIONS
let (x,y) = undefined in @"e"@

23

does not cause an execution-time error until x or y is evaluated.

Translation: The dynamic semantics of the expression let { d1 ; . . . ; dn } in e0 are captured by this translation: After removing all type signatures, each declaration di is translated into an equation of the form pi = ei , where pi and ei are patterns and expressions respectively, using the translation in Section 4.4.3. Once done, these identities hold, which may be used as a translation into the kernel:
let {p1 =e1 ; ... ; pn =en } in e0 let p = e1 in e0 let p = e1 in e0 = = = let (˜p1 , ... ,˜pn ) = (e1 , ... ,en ) in e0 case e1 of ˜p -> e0 where no variable in p appears free in e1 let p = fix ( \ ˜p -> e1 ) in e0

where fix is the least ﬁxpoint operator. Note the use of the irrefutable patterns ˜p. This translation does not preserve the static semantics because the use of case precludes a fully polymorphic typing of the bound variables. The static semantics of the bindings in a let expression are described in Section 4.4.3.

A case expression has the general form case e of { p1 match1 ; . . . ; pn matchn } where each matchi is of the general form | gsi1 -> ei1 ... | gsimi -> eimi where declsi (Notice that in the syntax rule for guards, the “|” is a terminal symbol, not the syntactic metasymbol for alternation.) Each alternative pi matchi consists of a pattern pi and its matches, matchi . Each match in turn consists of a sequence of pairs of guards gsij and bodies eij (expressions), followed by optional bindings (declsi ) that scope over all of the guards and expressions of the alternative. A guard has one of the following forms:

24

CHAPTER 3. EXPRESSIONS • pattern guards are of the form p <- e, where p is a pattern (see Section 3.17) of type t and e is an expression type t 1 . They succeed if the expression e matches the pattern p, and introduce the bindings of the pattern to the environment. • local bindings are of the form let decls. They always succeed, and they introduce the names deﬁned in decls to the environment. • boolean guards are arbitrary expressions of type Bool. They succeed if the expression evaluates to True, and they do not introduce new names to the environment. A boolean guard, g, is semantically equivalent to the pattern guard True <- g.

An alternative of the form pat -> exp where decls is treated as shorthand for: pat | True -> exp where decls A case expression must have at least one alternative and each alternative must have at least one body. Each body must have the same type, and the type of the whole expression is that type. A case expression is evaluated by pattern matching the expression e against the individual alternatives. The alternatives are tried sequentially, from top to bottom. If e matches the pattern of an alternative, then the guarded expressions for that alternative are tried sequentially from top to bottom in the environment of the case expression extended ﬁrst by the bindings created during the matching of the pattern, and then by the declsi in the where clause associated with that alternative. For each guarded expression, the comma-separated guards are tried sequentially from left to right. If all of them succeed, then the corresponding expression is evaluated in the environment extended with the bindings introduced by the guards. That is, the bindings that are introduced by a guard (either by using a let clause or a pattern guard) are in scope in the following guards and the corresponding expression. If any of the guards fail, then this guarded expression fails and the next guarded expression is tried. If none of the guarded expressions for a given alternative succeed, then matching continues with the next alternative. If no alternative succeeds, then the result is ⊥. Pattern matching is described in Section 3.17, with the formal semantics of case expressions in Section 3.17.3. A note about parsing. The expression
case x of { (a,_) | let b = not a in b :: Bool -> a }

is tricky to parse correctly. It has a single unambiguous parse, namely
case x of { (a,_) | (let b = not a in b :: Bool) -> a }

However, the phrase Bool -> a is syntactically valid as a type, and parsers with limited lookahead may incorrectly commit to this choice, and hence reject the program. Programmers are advised, therefore, to avoid guards that end with a type signature — indeed that is why a guard contains an inﬁxexp not an exp.
1 Note that the syntax of a pattern guard is the same as that of a generator in a list comprehension. The contextual difference is that, in a list comprehension, a pattern of type t goes with an expression of type [t].

A do expression provides a more conventional syntax for monadic programming. It allows an expression such as
putStr "x: " >> getLine >>= \l -> return (words l)

to be written in a more traditional way as:
do putStr "x: " l <- getLine return (words l)

Translation: Do expressions satisfy these identities, which may be used as a translation into the kernel, after eliminating empty stmts: do {e} do {e;stmts} do {p <- e; stmts} = = = e e >> do {stmts} let ok p = do {stmts} ok _ = fail "..." in e >>= ok let decls in do {stmts}

do {let decls; stmts}

=

The ellipsis "..." stands for a compiler-generated error message, passed to fail, preferably giving some indication of the location of the pattern-match failure; the functions >>, >>=, and fail are operations in the class Monad, as deﬁned in the Prelude; and ok is a fresh identiﬁer. As indicated by the translation of do, variables bound by let have fully polymorphic types while those deﬁned by <- are lambda bound and are thus monomorphic.

3.15

Datatypes with Field Labels

A datatype declaration may optionally deﬁne ﬁeld labels (see Section 4.2.1). These ﬁeld labels can be used to construct, select from, and update ﬁelds in a manner that is independent of the overall structure of the datatype. Different datatypes cannot share common ﬁeld labels in the same scope. A ﬁeld label can be used at most once in a constructor. Within a datatype, however, a ﬁeld label can be used in more than one constructor provided the ﬁeld has the same typing in all constructors. To illustrate the last point, consider:

Here S is legal but T is not, because y is given inconsistent typings in the latter.

3.15.1
aexp

Field Selection
→ qvar

Field labels are used as selector functions. When used as a variable, a ﬁeld label serves as a function that extracts the ﬁeld from an object. Selectors are top level bindings and so they may be shadowed by local variables but cannot conﬂict with other top level bindings of the same name. This shadowing only affects selector functions; in record construction (Section 3.15.2) and update (Section 3.15.3), ﬁeld labels cannot be confused with ordinary variables.

where C1 . . . Cn are all the constructors of the datatype containing a ﬁeld labeled with f , pij is y when f labels the j th component of Ci or _ otherwise, and ei is y when some ﬁeld in Ci has a label of f or undefined otherwise.

A constructor with labeled ﬁelds may be used to construct a value in which the components are speciﬁed by name rather than by position. Unlike the braces used in declaration lists, these are not subject to layout; the { and } characters must be explicit. (This is also true of ﬁeld updates and ﬁeld patterns.) Construction using ﬁeld labels is subject to the following constraints: • Only ﬁeld labels declared with the speciﬁed constructor may be mentioned. • A ﬁeld label may not be mentioned more than once. • Fields not mentioned are initialized to ⊥. • A compile-time error occurs when any strict ﬁelds (ﬁelds whose declared types are preﬁxed by !) are omitted during construction. Strict ﬁelds are discussed in Section 4.2.1. The expression F {}, where F is a data constructor, is legal whether or not F was declared with record syntax (provided F has no strict ﬁelds — see the third bullet above); it denotes F ⊥1 . . . ⊥n , where n is the arity of F.

where k is the arity of C . The auxiliary function pickiC bs d is deﬁned as follows: If the i th component of a constructor C has the ﬁeld label f , and if f = v appears in the binding list bs, then pickiC bs d is v . Otherwise, pickiC bs d is the default value d .

3.15.3
aexp

Updates Using Field Labels
→ aexp
qcon

{ fbind1 , . . . , fbindn }

(labeled update, n ≥ 1 )

Values belonging to a datatype with ﬁeld labels may be non-destructively updated. This creates a new value in which the speciﬁed ﬁeld values replace those in the existing value. Updates are restricted in the following ways: • All labels must be taken from the same datatype. • At least one constructor must deﬁne all of the labels mentioned in the update. • No label may be mentioned more than once. • An execution error occurs when the value being updated does not contain all of the speciﬁed labels. Translation: Using the prior deﬁnition of pick , = case e of
C C C1 v1 . . . vk1 -> C1 (pick1 1 bs v1 ) . . . (pickk11 bs vk1 ) ... C C Cj v1 . . . vkj -> Cj (pick1 j bs v1 ) . . . (pickkj j bs vkj ) _ -> error "Update error"

The ﬁeld f1 is common to both constructors in T. This example translates expressions using constructors in ﬁeld-label notation into equivalent expressions using the same constructors without ﬁeld labels. A compile-time error will result if no single constructor deﬁnes the set of ﬁeld labels used in an update, such as x {f2 = 1, f3 = ’x’}.

28

CHAPTER 3. EXPRESSIONS

3.16
exp

Expression Type-Signatures
→ exp :: [context =>] type

Expression type-signatures have the form e :: t, where e is an expression and t is a type (Section 4.1.2); they are used to type an expression explicitly and may be used to resolve ambiguous typings due to overloading (see Section 4.3.4). The value of the expression is just that of exp. As with normal type signatures (see Section 4.4.1), the declared type may be more speciﬁc than the principal type derivable from exp, but it is an error to give a type that is more general than, or not comparable to, the principal type. Translation: e :: t = let { v :: t; v = e } in v

3.17

Pattern Matching

Patterns appear in lambda abstractions, function deﬁnitions, pattern bindings, list comprehensions, do expressions, and case expressions. However, the ﬁrst ﬁve of these ultimately translate into case expressions, so deﬁning the semantics of pattern matching for case expressions is sufﬁcient.

The arity of a constructor must match the number of sub-patterns associated with it; one cannot match against a partially-applied constructor. All patterns must be linear —no variable may appear more than once. For example, this deﬁnition is illegal:

Patterns of the form _ are wildcards and are useful when some part of a pattern is not referenced on the right-hand-side. It is as if an identiﬁer not used elsewhere were put in its place. For example,
case e of { [x,_,_] -> if x==0 then True else False }

Patterns are matched against values. Attempting to match a pattern can have one of three results: it may fail; it may succeed, returning a binding for each variable in the pattern; or it may diverge (i.e. return ⊥). Pattern matching proceeds from left to right, and outside to inside, according to the following rules: 1. Matching the pattern var against a value v always succeeds and binds var to v . 2. Matching the pattern ˜apat against a value v always succeeds. The free variables in apat are bound to the appropriate values if matching apat against v would otherwise succeed, and to ⊥ if matching apat against v fails or diverges. (Binding does not imply evaluation.) Operationally, this means that no matching is done on a ˜apat pattern until one of the variables in apat is used. At that point the entire pattern is matched against the value, and if the match fails or diverges, so does the overall computation. 3. Matching the wildcard pattern _ against any value always succeeds, and no binding is done. 4. Matching the pattern con pat against a value, where con is a constructor deﬁned by newtype, depends on the value: • If the value is of the form con v , then pat is matched against v . • If the value is ⊥, then pat is matched against ⊥. That is, constructors associated with newtype serve only to change the type of a value. 5. Matching the pattern con pat1 . . . patn against a value, where con is a constructor deﬁned by data, depends on the value:

30

CHAPTER 3. EXPRESSIONS • If the value is of the form con v1 . . . vn , sub-patterns are matched left-to-right against the components of the data value; if all matches succeed, the overall match succeeds; the ﬁrst to fail or diverge causes the overall match to fail or diverge, respectively. • If the value is of the form con v1 . . . vm , where con is a different constructor to con , the match fails. • If the value is ⊥, the match diverges. 6. Matching against a constructor using labeled ﬁelds is the same as matching ordinary constructor patterns except that the ﬁelds are matched in the order they are named in the ﬁeld list. All ﬁelds listed must be declared by the constructor; ﬁelds may not be named more than once. Fields not named by the pattern are ignored (matched against _). 7. Matching a numeric, character, or string literal pattern k against a value v succeeds if v == k , where == is overloaded based on the type of the pattern. The match diverges if this test diverges. The interpretation of numeric literals is exactly as described in Section 3.2; that is, the overloaded function fromInteger or fromRational is applied to an Integer or Rational literal (resp) to convert it to the appropriate type. 8. Matching an as-pattern var @apat against a value v is the result of matching apat against v , augmented with the binding of var to v . If the match of apat against v fails or diverges, then so does the overall match.

Aside from the obvious static type constraints (for example, it is a static error to match a character against a boolean), the following static class constraints hold: • An integer literal pattern can only be matched against a value in the class Num. • A ﬂoating literal pattern can only be matched against a value in the class Fractional. It is sometimes helpful to distinguish two kinds of patterns. Matching an irrefutable pattern is non-strict: the pattern matches even if the value to be matched is ⊥. Matching a refutable pattern is strict: if the value to be matched is ⊥ the match diverges. The irrefutable patterns are as follows: a variable, a wildcard, N apat where N is a constructor deﬁned by newtype and apat is irrefutable (see Section 4.2.3), var @apat where apat is irrefutable, or of the form ˜apat (whether or not apat is irrefutable). All other patterns are refutable. Here are some examples: 1. If the pattern [’a’,’b’] is matched against [’x’,⊥], then ’a’ fails to match against ’x’, and the result is a failed match. But if [’a’,’b’] is matched against [⊥,’x’], then attempting to match ’a’ against ⊥ causes the match to diverge. 2. These examples demonstrate refutable vs. irrefutable matching: (\ ˜(x,y) -> 0) ⊥ (\ (x,y) -> 0) ⊥ (\ ˜[x] -> 0) [] (\ ˜[x] -> x) [] ⇒ ⇒ ⇒ ⇒ 0 ⊥ ⇒ ⇒ ⊥ ⊥:⊥:⊥ (0,1) ⊥ 0 ⊥

Additional examples may be found in Section 4.2.3. Top level patterns in case expressions and the set of top level patterns in function or pattern bindings may have zero or more associated guards. See Section 3.13 for the syntax and semantics of guards. The guard semantics have an inﬂuence on the strictness characteristics of a function or case expression. In particular, an otherwise irrefutable pattern may be evaluated because of a guard. For example, in
f :: (Int,Int,Int) -> [Int] -> Int f ˜(x,y,z) [a] | (a == y) = 1

both a and y will be evaluated by == in the guard.

3.17.3

Formal Semantics of Pattern Matching

The semantics of all pattern matching constructs other than case expressions are deﬁned by giving identities that relate those constructs to case expressions. The semantics of case expressions themselves are in turn given as a series of identities, in Figures 3.1–3.3. Any implementation should behave so that these identities hold; it is not expected that it will use them directly, since that would generate rather inefﬁcient code. In Figures 3.1–3.3: e, e and ei are expressions; gi and gsi are guards and sequences of guards respecively; p and pi are patterns; v , x , and xi are variables; K and K are algebraic datatype (data) constructors (including tuple constructors); and N is a newtype constructor. Rule (b) matches a general source-language case expression, regardless of whether it actually includes guards—if no guards are written, then True is substituted for the guards gsi,j in the matchi forms. Subsequent identities manipulate the resulting case expression into simpler and simpler forms. Rule (h) in Figure 3.2 involves the overloaded operator ==; it is this rule that deﬁnes the meaning of pattern matching against overloaded constants. These identities all preserve the static semantics. Rules (d), (e), (j), and (q) use a lambda rather than a let; this indicates that variables bound by case are monomorphically typed (Section 4.1.4).

The declarations in the syntactic category topdecls are only allowed at the top level of a Haskell module (see Chapter 5), whereas decls may be used either at the top level or in nested scopes (i.e. those within a let or where construct). For exposition, we divide the declarations into three groups: user-deﬁned datatypes, consisting of type, newtype, and data declarations (Section 4.2); type classes and overloading, consisting of class, instance, and default declarations (Section 4.3); and nested declarations, consisting of value bindings, type signatures, and ﬁxity declarations (Section 4.4). Haskell has several primitive datatypes that are “hard-wired” (such as integers and ﬂoating-point numbers), but most “built-in” datatypes are deﬁned with normal Haskell code, using normal type and data declarations. These “built-in” datatypes are described in detail in Section 6.1.

4.1

Overview of Types and Classes

Haskell uses a traditional Hindley-Milner polymorphic type system to provide a static type semantics [4, 6], but the type system has been extended with type classes (or just classes) that provide a structured way to introduce overloaded functions. A class declaration (Section 4.3.1) introduces a new type class and the overloaded operations that must be supported by any type that is an instance of that class. An instance declaration (Section 4.3.2) declares that a type is an instance of a class and includes the deﬁnitions of the overloaded operations—called class methods—instantiated on the named type. For example, suppose we wish to overload the operations (+) and negate on types Int and Float. We introduce a new type class called Num:
class Num a where (+) :: a -> a -> a negate :: a -> a -- simplified class declaration for Num -- (Num is defined in the Prelude)

This declaration may be read “a type a is an instance of the class Num if there are class methods (+) and negate, of the given types, deﬁned on it.” We may then declare Int and Float to be instances of this class:
instance Num Int where -- simplified instance of Num Int x + y = addInt x y negate x = negateInt x instance Num Float where -- simplified instance of Num Float x + y = addFloat x y negate x = negateFloat x

4.1. OVERVIEW OF TYPES AND CLASSES

37

where addInt, negateInt, addFloat, and negateFloat are assumed in this case to be primitive functions, but in general could be any user-deﬁned function. The ﬁrst declaration above may be read “Int is an instance of the class Num as witnessed by these deﬁnitions (i.e. class methods) for (+) and negate.” More examples of type classes can be found in the papers by Jones [8] or Wadler and Blott [13]. The term ‘type class’ was used to describe the original Haskell 1.0 type system; ‘constructor class’ was used to describe an extension to the original type classes. There is no longer any reason to use two different terms: in this report, ‘type class’ includes both the original Haskell type classes and the constructor classes introduced by Jones.

4.1.1

Kinds

To ensure that they are valid, type expressions are classiﬁed into different kinds, which take one of two possible forms: • The symbol ∗ represents the kind of all nullary type constructors. • If κ1 and κ2 are kinds, then κ1 → κ2 is the kind of types that take a type of kind κ1 and return a type of kind κ2 . Kind inference checks the validity of type expressions in a similar way that type inference checks the validity of value expressions. However, unlike types, kinds are entirely implicit and are not a visible part of the language. Kind inference is discussed in Section 4.6.

The syntax for Haskell type expressions is given above. Just as data values are built using data constructors, type values are built from type constructors. As with data constructors, the names of type constructors start with uppercase letters. Unlike data constructors, inﬁx type constructors are not allowed (other than (->)). The main forms of type expression are as follows:

38

CHAPTER 4. DECLARATIONS AND BINDINGS 1. Type variables, written as identiﬁers beginning with a lowercase letter. The kind of a variable is determined implicitly by the context in which it appears. 2. Type constructors. Most type constructors are written as an identiﬁer beginning with an uppercase letter. For example: • Char, Int, Integer, Float, Double and Bool are type constants with kind ∗. • Maybe and IO are unary type constructors, and treated as types with kind ∗ → ∗. • The declarations data T ... or newtype T ... add the type constructor T to the type vocabulary. The kind of T is determined by kind inference. Special syntax is provided for certain built-in type constructors: • The trivial type is written as () and has kind ∗. It denotes the “nullary tuple” type, and has exactly one value, also written () (see Sections 3.9 and 6.1.5). • The function type is written as (->) and has kind ∗ → ∗ → ∗. • The list type is written as [] and has kind ∗ → ∗. • The tuple types are written as (,), (,,), and so on. Their kinds are ∗ → ∗ → ∗, ∗ → ∗ → ∗ → ∗, and so on. Use of the (->) and [] constants is described in more detail below. 3. Type application. If t1 is a type of kind κ1 → κ2 and t2 is a type of kind κ1 , then t1 t2 is a type expression of kind κ2 . 4. A parenthesized type, having form (t), is identical to the type t.

For example, the type expression IO a can be understood as the application of a constant, IO, to the variable a. Since the IO type constructor has kind ∗ → ∗, it follows that both the variable a and the whole expression, IO a, must have kind ∗. In general, a process of kind inference (see Section 4.6) is needed to determine appropriate kinds for user-deﬁned datatypes, type synonyms, and classes. Special syntax is provided to allow certain type expressions to be written in a more traditional style: 1. A function type has the form t1 -> t2 , which is equivalent to the type (->) t1 t2 . Function arrows associate to the right. For example, Int -> Int -> Float means Int -> (Int -> Float). 2. A tuple type has the form (t1 , . . . , tk ) where k ≥ 2 , which is equivalent to the type (,. . . ,) t1 . . . tk where there are k − 1 commas between the parenthesis. It denotes the type of k -tuples with the ﬁrst component of type t1 , the second component of type t2 , and so on (see Sections 3.8 and 6.1.4). 3. A list type has the form [t], which is equivalent to the type [] t. It denotes the type of lists with elements of type t (see Sections 3.7 and 6.1.3). These special syntactic forms always denote the built-in type constructors for functions, tuples, and lists, regardless of what is in scope. In a similar way, the preﬁx type constructors (->), [], (), (,), and so on, always denote the built-in type constructors; they cannot be qualiﬁed, nor mentioned in import or export lists (Chapter 5). (Hence the special production, “gtycon”, above.) Although the list and tuple types have special syntax, their semantics is the same as the equivalent user-deﬁned algebraic data types.

4.1. OVERVIEW OF TYPES AND CLASSES

39

Notice that expressions and types have a consistent syntax. If ti is the type of expression or pattern ei , then the expressions (\ e1 -> e2 ), [e1 ], and (e1 , e2 ) have the types (t1 -> t2 ), [t1 ], and (t1 , t2 ), respectively. With one exception (that of the distinguished type variable in a class declaration (Section 4.3.1)), the type variables in a Haskell type expression are all assumed to be universally quantiﬁed; there is no explicit syntax for universal quantiﬁcation [4]. For example, the type expression a -> a denotes the type ∀ a. a → a. For clarity, however, we often write quantiﬁcation explicitly when discussing the types of Haskell programs. When we write an explicitly quantiﬁed type, the scope of the ∀ extends as far to the right as possible; for example, ∀ a. a → a means ∀ a. (a → a).

A class assertion has form qtycls tyvar , and indicates the membership of the type tyvar in the class qtycls. A class identiﬁer begins with an uppercase letter. A context consists of zero or more class assertions, and has the general form ( C1 u1 , . . . , Cn un ) where C1 , . . . , Cn are class identiﬁers, and each of the u1 , . . . , un is either a type variable, or the application of type variable to one or more types. The outer parentheses may be omitted when n = 1 . In general, we use cx to denote a context and we write cx => t to indicate the type t restricted by the context cx . The context cx must only contain type variables referenced in t. For convenience, we write cx => t even if the context cx is empty, although in this case the concrete syntax contains no =>.

4.1.4

Semantics of Types and Classes

In this section, we provide informal details of the type system. (Wadler and Blott [13] and Jones [8] discuss type and constructor classes, respectively, in more detail.) The Haskell type system attributes a type to each expression in the program. In general, a type is of the form ∀ u. cx ⇒ t, where u is a set of type variables u1 , . . . , un . In any such type, any of the universallyquantiﬁed type variables ui that are free in cx must also be free in t. Furthermore, the context cx must be of the form given above in Section 4.1.3. For example, here are some valid types:
Eq a => a -> a (Eq a, Show a, Eq b) => [a] -> [b] -> String (Eq (f a), Functor f) => (a -> b) -> f a -> f b -> Bool

In the third type, the constraint Eq (f a) cannot be made simpler because f is universally quantiﬁed.

40

CHAPTER 4. DECLARATIONS AND BINDINGS

The type of an expression e depends on a type environment that gives types for the free variables in e, and a class environment that declares which types are instances of which classes (a type becomes an instance of a class only via the presence of an instance declaration or a deriving clause). Types are related by a generalization preorder (speciﬁed below); the most general type, up to the equivalence induced by the generalization preorder, that can be assigned to a particular expression (in a given environment) is called its principal type. Haskell’s extended Hindley-Milner type system can infer the principal type of all expressions, including the proper use of overloaded class methods (although certain ambiguous overloadings could arise, as described in Section 4.3.4). Therefore, explicit typings (called type signatures) are usually optional (see Sections 3.16 and 4.4.1). The type ∀ u. cx1 ⇒ t1 is more general than the type ∀ w . cx2 ⇒ t2 if and only if there is a substitution S whose domain is u such that: • t2 is identical to S (t1 ). • Whenever cx2 holds in the class environment, S (cx1 ) also holds. A value of type ∀ u. cx ⇒ t, may be instantiated at types s if and only if the context cx [s/u] holds. For example, consider the function double:
double x = x + x

The most general type of double is ∀ a. Num a ⇒ a → a. double may be applied to values of type Int (instantiating a to Int), since Num Int holds, because Int is an instance of the class Num. However, double may not normally be applied to values of type Char, because Char is not normally an instance of class Num. The user may choose to declare such an instance, in which case double may indeed be applied to a Char.

4.2

User-Deﬁned Datatypes

In this section, we describe algebraic datatypes (data declarations), renamed datatypes (newtype declarations), and type synonyms (type declarations). These declarations may only appear at the top level of a module.

The precedence for constr is the same as that for expressions—normal constructor application has higher precedence than inﬁx constructor application (thus a : Foo a parses as a : (Foo a)). An algebraic datatype declaration has the form: data cx => T u1 . . . uk = K1 t11 . . . t1k1 | · · · | Kn tn1 . . . tnkn where cx is a context. This declaration introduces a new type constructor T with zero or more constituent data constructors K1 , . . . , Kn . In this Report, the unqualiﬁed term “constructor” always means “data constructor”. The types of the data constructors are given by: Ki :: ∀ u1 . . . uk . cxi ⇒ ti1 → · · · → tiki → (T u1 . . . uk ) where cxi is the largest subset of cx that constrains only those type variables free in the types ti1 , . . . , tiki . The type variables u1 through uk must be distinct and may appear in cx and the tij ; it is a static error for any other type variable to appear in cx or on the right-hand-side. The new type constant T has a kind of the form κ1 → . . . → κk → ∗ where the kinds κi of the argument variables ui are determined by kind inference as described in Section 4.6. This means that T may be used in type expressions with anywhere between 0 and k arguments. For example, the declaration
data Eq a => Set a = NilSet | ConsSet a (Set a)

introduces a type constructor Set of kind ∗ → ∗, and constructors NilSet and ConsSet with types NilSet :: ∀ a. Set a ConsSet :: ∀ a. Eq a ⇒ a → Set a → Set a In the example given, the overloaded type for ConsSet ensures that ConsSet can only be applied to values whose type is an instance of the class Eq. Pattern matching against ConsSet also gives rise to an Eq a constraint. For example:
f (ConsSet a s) = a

the function f has inferred type Eq a => Set a -> a. The context in the data declaration has no other effect whatsoever. The visibility of a datatype’s constructors (i.e. the “abstractness” of the datatype) outside of the module in which the datatype is deﬁned is controlled by the form of the datatype’s name in the export list as described in Section 5.8. The optional deriving part of a data declaration has to do with derived instances, and is described in Section 4.3.3.

Labelled Fields A data constructor of arity k creates an object with k components. These components are normally accessed positionally as arguments to the constructor in expressions or patterns. For large datatypes it is useful to assign ﬁeld labels to the components of a data object. This allows a speciﬁc ﬁeld to be referenced independently of its location within the constructor.

42

CHAPTER 4. DECLARATIONS AND BINDINGS

A constructor deﬁnition in a data declaration may assign labels to the ﬁelds of the constructor, using the record syntax (C { ... }). Constructors using ﬁeld labels may be freely mixed with constructors without them. A constructor with associated ﬁeld labels may still be used as an ordinary constructor; features using labels are simply a shorthand for operations using an underlying positional constructor. The arguments to the positional constructor occur in the same order as the labeled ﬁelds. For example, the declaration
data C = F { f1,f2 :: Int, f3 :: Bool }

deﬁnes a type and constructor identical to the one produced by
data C = F Int Int Bool

Operations using ﬁeld labels are described in Section 3.15. A data declaration may use the same ﬁeld label in multiple constructors as long as the typing of the ﬁeld is the same in all cases after type synonym expansion. A label cannot be shared by more than one type in scope. Field names share the top level namespace with ordinary variables and class methods and must not conﬂict with other top level names in scope. The pattern F {} matches any value built with constructor F, whether or not F was declared with record syntax.

Strictness Flags Whenever a data constructor is applied, each argument to the constructor is evaluated if and only if the corresponding type in the algebraic datatype declaration has a strictness ﬂag, denoted by an exclamation point, “!”. Lexically, “!” is an ordinary varsym not a reservedop; it has special signiﬁcance only in the context of the argument types of a data declaration. Translation: A declaration of the form data cx => T u1 . . . uk = . . . | K s1 . . . sn | . . . where each si is either of the form !ti or ti , replaces every occurrence of K in an expression by (\ x1 . . . xn -> ( ((K op1 x1 ) op2 x2 ) . . . ) opn xn ) where opi is the non-strict apply function $ if si is of the form ti , and opi is the strict apply function $! (see Section 6.2) if si is of the form ! ti . Pattern matching on K is not affected by strictness ﬂags.

A type synonym declaration introduces a new type that is equivalent to an old type. It has the form type T u1 . . . uk = t which introduces a new type constructor, T . The type (T t1 . . . tk ) is equivalent to the type t[t1 /u1 , . . . , tk /uk ]. The type variables u1 through uk must be distinct and are scoped only over t; it is a static error for any other type variable to appear in t. The kind of the new type constructor T is of the form κ1 → . . . → κk → κ where the kinds κi of the arguments ui and κ of the right hand side t are determined by kind inference as described in Section 4.6. For example, the following deﬁnition can be used to provide an alternative way of writing the list type constructor:

4.2. USER-DEFINED DATATYPES
type List = []

43

Type constructor symbols T introduced by type synonym declarations cannot be partially applied; it is a static error to use T without the full number of arguments. Although recursive and mutually recursive datatypes are allowed, this is not so for type synonyms, unless an algebraic datatype intervenes. For example,
type Rec a data Circ a = = [Circ a] Tag [Rec a]

is not. Similarly, type Rec a = [Rec a] is not allowed. Type synonyms are a convenient, but strictly syntactic, mechanism to make type signatures more readable. A synonym and its deﬁnition are completely interchangeable, except in the instance type of an instance declaration (Section 4.3.2).

A declaration of the form newtype cx => T u1 . . . uk = N t introduces a new type whose representation is the same as an existing type. The type (T u1 . . . uk ) renames the datatype t. It differs from a type synonym in that it creates a distinct type that must be explicitly coerced to or from the original type. Also, unlike type synonyms, newtype may be used to deﬁne recursive types. The constructor N in an expression coerces a value from type t to type (T u1 . . . uk ). Using N in a pattern coerces a value from type (T u1 . . . uk ) to type t. These coercions may be implemented without execution time overhead; newtype does not change the underlying representation of an object. New instances (see Section 4.3.2) can be deﬁned for a type deﬁned by newtype but may not be deﬁned for a type synonym. A type created by newtype differs from an algebraic datatype in that the representation of an algebraic datatype has an extra level of indirection. This difference may make access to the representation less efﬁcient. The difference is reﬂected in different rules for pattern matching (see Section 3.17). Unlike algebraic datatypes, the newtype constructor N is unlifted, so that N ⊥ is the same as ⊥. The following examples clarify the differences between data (algebraic datatypes), type (type synonyms), and newtype (renaming types.) Given the declarations

the expressions (d1 ⊥), (d2 ⊥) and (d2 (D2 ⊥)) are all equivalent to ⊥, whereas (n ⊥), (n (N ⊥)), (d1 (D1 ⊥)) and (s ⊥) are all equivalent to 42. In particular, (N ⊥) is equivalent to ⊥ while (D1 ⊥) is not equivalent to ⊥. The optional deriving part of a newtype declaration is treated in the same way as the deriving component of a data declaration; see Section 4.3.3. A newtype declaration may use ﬁeld-naming syntax, though of course there may only be one ﬁeld. Thus:
newtype Age = Age { unAge :: Int }

brings into scope both a constructor and a de-constructor:
Age :: Int -> Age unAge :: Age -> Int

A class declaration introduces a new class and the operations (class methods) on it. A class declaration has the general form: class cx => C u where cdecls This introduces a new class name C ; the type variable u is scoped only over the class method signatures in the class body. The context cx speciﬁes the superclasses of C , as described below; the only type variable that may be referred to in cx is u. The superclass relation must not be cyclic; i.e. it must form a directed acyclic graph. The cdecls part of a class declaration contains three kinds of declarations:

4.3. TYPE CLASSES AND OVERLOADING

45

• The class declaration introduces new class methods vi , whose scope extends outside the class declaration. The class methods of a class declaration are precisely the vi for which there is an explicit type signature vi :: cxi => ti in cdecls. Class methods share the top level namespace with variable bindings and ﬁeld names; they must not conﬂict with other top level bindings in scope. That is, a class method can not have the same name as a top level deﬁnition, a ﬁeld name, or another class method. The type of the top-level class method vi is: vi :: ∀u, w. (Cu, cxi ) ⇒ ti The ti must mention u; it may mention type variables w other than u, in which case the type of vi is polymorphic in both u and w . The cxi may constrain only w ; in particular, the cxi may not constrain u. For example:
class Foo a where op :: Num b => a -> b -> a

Here the type of op is ∀ a, b. (Foo a, Num b) ⇒ a → b → a. • The cdecls may also contain a ﬁxity declaration for any of the class methods (but for no other values). However, since class methods declare top-level values, the ﬁxity declaration for a class method may alternatively appear at top level, outside the class declaration. • Lastly, the cdecls may contain a default class method for any of the vi . The default class method for vi is used if no binding for it is given in a particular instance declaration (see Section 4.3.2). The default method declaration is a normal value deﬁnition, except that the left hand side may only be a variable or function deﬁnition. For example:
class Foo a where op1, op2 :: a -> a (op1, op2) = ...

is not permitted, because the left hand side of the default declaration is a pattern. Other than these cases, no other declarations are permitted in cdecls. A class declaration with no where part may be useful for combining a collection of classes into a larger one that inherits all of the class methods in the original ones. For example:
class (Read a, Show a) => Textual a

In such a case, if a type is an instance of all superclasses, it is not automatically an instance of the subclass, even though the subclass has no immediate class methods. The instance declaration must be given explicitly with no where part.

An instance declaration introduces an instance of a class. Let class cx => C u where { cbody } be a class declaration. The general form of the corresponding instance declaration is: instance cx => C (T u1 . . . uk ) where { d } where k ≥ 0 . The type (T u1 . . . uk ) must take the form of a type constructor T applied to simple type variables u1 , . . . uk ; furthermore, T must not be a type synonym, and the ui must all be distinct. This prohibits instance declarations such as:
instance C (a,a) where ... instance C (Int,a) where ... instance C [[a]] where ...

The declarations d may contain bindings only for the class methods of C . It is illegal to give a binding for a class method that is not in scope, but the name under which it is in scope is immaterial; in particular, it may be a qualiﬁed name. (This rule is identical to that used for subordinate names in export lists — Section 5.2.) For example, this is legal, even though range is in scope only with the qualiﬁed name Data.Ix.range.
module A where import qualified Data.Ix instance Data.Ix.Ix T where range = ...

The declarations may not contain any type signatures or ﬁxity declarations, since these have already been given in the class declaration. As in the case of default class methods (Section 4.3.1), the method declarations must take the form of a variable or function deﬁnition. If no binding is given for some class method then the corresponding default class method in the class declaration is used (if present); if such a default does not exist then the class method of this instance is bound to undefined and no compile-time error results. An instance declaration that makes the type T to be an instance of class C is called a C-T instance declaration and is subject to these static restrictions: • A type may not be declared as an instance of a particular class more than once in the program. • The class and type must have the same kind; this can be determined using kind inference as described in Section 4.6. • Assume that the type variables in the instance type (T u1 . . . uk ) satisfy the constraints in the instance context cx . Under this assumption, the following two conditions must also be satisﬁed:

4.3. TYPE CLASSES AND OVERLOADING

47

1. The constraints expressed by the superclass context cx [(T u1 . . . uk )/u] of C must be satisﬁed. In other words, T must be an instance of each of C ’s superclasses and the contexts of all superclass instances must be implied by cx . 2. Any constraints on the type variables in the instance type that are required for the class method declarations in d to be well-typed must also be satisﬁed. In fact, except in pathological cases it is possible to infer from the instance declaration the most general instance context cx satisfying the above two constraints, but it is nevertheless mandatory to write an explicit instance context. The following example illustrates the restrictions imposed by superclass instances:
class Foo a => Bar a where ... instance (Eq a, Show a) => Foo [a] where ... instance Num a => Bar [a] where ...

This example is valid Haskell. Since Foo is a superclass of Bar, the second instance declaration is only valid if [a] is an instance of Foo under the assumption Num a. The ﬁrst instance declaration does indeed say that [a] is an instance of Foo under this assumption, because Eq and Show are superclasses of Num. If the two instance declarations instead read like this:
instance Num a => Foo [a] where ... instance (Eq a, Show a) => Bar [a] where ...

then the program would be invalid. The second instance declaration is valid only if [a] is an instance of Foo under the assumptions (Eq a, Show a). But this does not hold, since [a] is only an instance of Foo under the stronger assumption Num a. Further examples of instance declarations may be found in Chapter 9.

4.3.3

Derived Instances

As mentioned in Section 4.2.1, data and newtype declarations contain an optional deriving form. If the form is included, then derived instance declarations are automatically generated for the datatype in each of the named classes. These instances are subject to the same restrictions as user-deﬁned instances. When deriving a class C for a type T , instances for all superclasses of C must exist for T , either via an explicit instance declaration or by including the superclass in the deriving clause. Derived instances provide convenient commonly-used operations for user-deﬁned datatypes. For example, derived instances for datatypes in the class Eq deﬁne the operations == and /=, freeing the programmer from the need to deﬁne them. The only classes in the Prelude for which derived instances are allowed are Eq, Ord, Enum, Bounded, Show, and Read, all mentioned in Figure 6.1. The precise details of how the derived instances are generated for each of these classes are provided in Chapter 11, including a speciﬁcation of when such derived instances are possible. Classes deﬁned by the standard libraries may also be derivable.

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A static error results if it is not possible to derive an instance declaration over a class named in a deriving form. For example, not all datatypes can properly support class methods in Enum. It is also a static error to give an explicit instance declaration for a class that is also derived. If the deriving form is omitted from a data or newtype declaration, then no instance declarations are derived for that datatype; that is, omitting a deriving form is equivalent to including an empty deriving form: deriving ().

A problem inherent with Haskell-style overloading is the possibility of an ambiguous type. For example, using the read and show functions deﬁned in Chapter 11, and supposing that just Int and Bool are members of Read and Show, then the expression
let x = read "..." in show x -- invalid

is ambiguous, because the types for show and read, show read :: ∀ a. Show a ⇒ a → String :: ∀ a. Read a ⇒ String → a

could be satisﬁed by instantiating a as either Int in both cases, or Bool. Such expressions are considered ill-typed, a static error. We say that an expression e has an ambiguous type if, in its type ∀ u. cx ⇒ t, there is a type variable u in u that occurs in cx but not in t. Such types are invalid. For example, the earlier expression involving show and read has an ambiguous type since its type is ∀ a. Show a, Read a ⇒ String. Ambiguous types can only be circumvented by input from the user. One way is through the use of expression type-signatures as described in Section 3.16. For example, for the ambiguous expression given earlier, one could write:
let x = read "..." in show (x::Bool)

which disambiguates the type. Occasionally, an otherwise ambiguous expression needs to be made the same type as some variable, rather than being given a ﬁxed type with an expression type-signature. This is the purpose of the function asTypeOf (Chapter 9): x ‘asTypeOf‘ y has the value of x , but x and y are forced to have the same type. For example,
approxSqrt x = encodeFloat 1 (exponent x ‘div‘ 2) ‘asTypeOf‘ x

(See Section 6.4.6 for a description of encodeFloat and exponent.) Ambiguities in the class Num are most common, so Haskell provides another way to resolve them—with a default declaration: default (t1 , . . . , tn ) where n ≥ 0 , and each ti must be a type for which Num ti holds. In situations where an ambiguous type is discovered, an ambiguous type variable, v , is defaultable if:

4.4. NESTED DECLARATIONS • v appears only in constraints of the form C v , where C is a class, and • at least one of these classes is a numeric class, (that is, Num or a subclass of Num), and

49

• all of these classes are deﬁned in the Prelude or a standard library (Figures 6.2–6.3 show the numeric classes, and Figure 6.1 shows the classes deﬁned in the Prelude.) Each defaultable variable is replaced by the ﬁrst type in the default list that is an instance of all the ambiguous variable’s classes. It is a static error if no such type is found. Only one default declaration is permitted per module, and its effect is limited to that module. If no default declaration is given in a module then it assumed to be:
default (Integer, Double)

The empty default declaration, default (), turns off all defaults in a module.

4.4

Nested Declarations

The following declarations may be used in any declaration list, including the top level of a module.

4.4.1
gendecl vars

Type Signatures
→ → vars :: [context =>] type var1 , . . . , varn

(n ≥ 1 )

A type signature speciﬁes types for variables, possibly with respect to a context. A type signature has the form: v1 , . . . , vn :: cx => t which is equivalent to asserting vi :: cx => t for each i from 1 to n. Each vi must have a value binding in the same declaration list that contains the type signature; i.e. it is invalid to give a type signature for a variable bound in an outer scope. Moreover, it is invalid to give more than one type signature for one variable, even if the signatures are identical. As mentioned in Section 4.1.2, every type variable appearing in a signature is universally quantiﬁed over that signature, and hence the scope of a type variable is limited to the type signature that contains it. For example, in the following declarations
f :: a -> a f x = x :: a

-- invalid

the a’s in the two type signatures are quite distinct. Indeed, these declarations contain a static error, since x does not have type ∀ a. a. (The type of x is dependent on the type of f; there is currently no way in Haskell to specify a signature for a variable with a dependent type; this is explained in Section 4.5.4.) If a given program includes a signature for a variable f , then each use of f is treated as having the declared type. It is a static error if the same type cannot also be inferred for the deﬁning occurrence of f .

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If a variable f is deﬁned without providing a corresponding type signature declaration, then each use of f outside its own declaration group (see Section 4.5) is treated as having the corresponding inferred, or principal type . However, to ensure that type inference is still possible, the deﬁning occurrence, and all uses of f within its declaration group must have the same monomorphic type (from which the principal type is obtained by generalization, as described in Section 4.5.2). For example, if we deﬁne
sqr x = x*x

then the principal type is sqr :: ∀ a. Num a ⇒ a → a, which allows applications such as sqr 5 or sqr 0.1. It is also valid to declare a more speciﬁc type, such as
sqr :: Int -> Int

but now applications such as sqr 0.1 are invalid. Type signatures such as
sqr :: (Num a, Num b) => a -> b sqr :: a -> a -- invalid -- invalid

are invalid, as they are more general than the principal type of sqr. Type signatures can also be used to support polymorphic recursion. The following deﬁnition is pathological, but illustrates how a type signature can be used to specify a type more general than the one that would be inferred:
data T a = K (T Int) (T a) f :: T a -> a f (K x y) = if f x == 1 then f y else undefined

If we remove the signature declaration, the type of f will be inferred as T Int -> Int due to the ﬁrst recursive call for which the argument to f is T Int. Polymorphic recursion allows the user to supply the more general type signature, T a -> a.

A ﬁxity declaration gives the ﬁxity and binding precedence of one or more operators. The integer in a ﬁxity declaration must be in the range 0 to 9 . A ﬁxity declaration may appear anywhere that a type signature appears and, like a type signature, declares a property of a particular operator. Also like a type signature, a ﬁxity declaration can only occur in the same sequence of declarations as the declaration of the operator itself, and at most one ﬁxity declaration may be given for any operator. (Class methods are a minor exception; their ﬁxity declarations can occur either in the class declaration itself or at top level.) There are three kinds of ﬁxity, non-, left- and right-associativity (infix, infixl, and infixr, respectively), and ten precedence levels, 0 to 9 inclusive (level 0 binds least tightly, and level 9 binds most tightly). If

the digit is omitted, level 9 is assumed. Any operator lacking a ﬁxity declaration is assumed to be infixl 9 (See Section 3 for more on the use of ﬁxities). Table 4.1 lists the ﬁxities and precedences of the operators deﬁned in the Prelude. Fixity is a property of a particular entity (constructor or variable), just like its type; ﬁxity is not a property of that entity’s name. For example:
module Bar( op ) where infixr 7 ‘op‘ op = ... module Foo where import qualified Bar infix 3 ‘op‘ a ‘op‘ b = (a ‘Bar.op‘ b) + 1 f x = let p ‘op‘ q = (p ‘Foo.op‘ q) * 2 in ...

Here, ‘Bar.op‘ is infixr 7, ‘Foo.op‘ is infix 3, and the nested deﬁnition of op in f’s right-hand side has the default ﬁxity of infixl 9. (It would also be possible to give a ﬁxity to the nested deﬁnition of ‘op‘ with a nested ﬁxity declaration.)

We distinguish two cases within this syntax: a pattern binding occurs when the left hand side is a pat; otherwise, the binding is called a function binding. Either binding may appear at the top-level of a module or within a where or let construct.

4.4.3.1

Function bindings

A function binding binds a variable to a function value. The general form of a function binding for variable x is: x p11 . . . p1k match1 ... x pn1 . . . pnk matchn where each pij is a pattern, and where each matchi is of the general form: = ei where { declsi } or | gsi1 ... | gsimi = ei1 = eimi where { declsi }

and where n ≥ 1 , 1 ≤ i ≤ n, mi ≥ 1 . The former is treated as shorthand for a particular case of the latter, namely: | True = ei where { declsi } Note that all clauses deﬁning a function must be contiguous, and the number of patterns in each clause must be the same. The set of patterns corresponding to each match must be linear—no variable is allowed to appear more than once in the entire set. Alternative syntax is provided for binding functional values to inﬁx operators. For example, these three function deﬁnitions are all equivalent:
plus x y z = x+y+z x ‘plus‘ y = \ z -> x+y+z (x ‘plus‘ y) z = x+y+z

4.5. STATIC SEMANTICS OF FUNCTION AND PATTERN BINDINGS

53

Note that ﬁxity resolution applies to the inﬁx variants of the function binding in the same way as for expressions (Section 10.6). Applying ﬁxity resolution to the left side of the equals in a function binding must leave the varop being deﬁned at the top level. For example, if we are deﬁning a new operator ## with precedence 6, then this deﬁnition would be illegal:
a ## b : xs = exp

A pattern binding binds variables to values. A simple pattern binding has form p = e. The pattern p is matched “lazily” as an irrefutable pattern, as if there were an implicit ˜ in front of it. See the translation in Section 3.12. The general form of a pattern binding is p match, where a match is the same structure as for function bindings above; in other words, a pattern binding is: p | gs1 | gs2 ... | gsm where = e1 = e2 = em { decls }

The static semantics of the function and pattern bindings of a let expression or where clause are discussed in this section.

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4.5.1

Dependency Analysis

In general the static semantics are given by applying the normal Hindley-Milner inference rules. In order to increase polymorphism, these rules are applied to groups of bindings identiﬁed by a dependency analysis. A binding b1 depends on a binding b2 in the same list of declarations if either 1. b1 contains a free identiﬁer that has no type signature and is bound by b2 , or 2. b1 depends on a binding that depends on b2 . A declaration group is a minimal set of mutually dependent bindings. Hindley-Milner type inference is applied to each declaration group in dependency order. The order of declarations in where/let constructs is irrelevant.

4.5.2

Generalization

The Hindley-Milner type system assigns types to a let-expression in two stages: 1. The declaration groups are considered in dependency order. For each group, a type with no universal quantiﬁcation is inferred for each variable bound in the group. Then, all type variables that occur in these types are universally quantiﬁed unless they are associated with bound variables in the type environment; this is called generalization. 2. Finally, the body of the let-expression is typed. For example, consider the declaration
f x = let g y = (y,y) in ...

The type of g’s deﬁnition is a → (a, a). The generalization step attributes to g the polymorphic type ∀ a. a → (a, a), after which the typing of the “...” part can proceed. When typing overloaded deﬁnitions, all the overloading constraints from a single declaration group are collected together, to form the context for the type of each variable declared in the group. For example, in the deﬁnition:
f x = let g1 x y = if x>y then show x else g2 y x g2 p q = g1 q p in ...

The types of the deﬁnitions of g1 and g2 are both a → a → String, and the accumulated constraints are Ord a (arising from the use of >), and Show a (arising from the use of show). The type variables appearing in this collection of constraints are called the constrained type variables. The generalization step attributes to both g1 and g2 the type ∀ a. (Ord a, Show a) ⇒ a → a → String

4.5. STATIC SEMANTICS OF FUNCTION AND PATTERN BINDINGS

55

Notice that g2 is overloaded in the same way as g1 even though the occurrences of > and show are in the deﬁnition of g1. If the programmer supplies explicit type signatures for more than one variable in a declaration group, the contexts of these signatures must be identical up to renaming of the type variables.

4.5.3

Context Reduction Errors

As mentioned in Section 4.1.4, the context of a type may constrain only a type variable, or the application of a type variable to one or more types. Hence, types produced by generalization must be expressed in a form in which all context constraints have be reduced to this “head normal form”. Consider, for example, the deﬁnition:
f xs y = xs == [y]

Its type is given by
f :: Eq a => [a] -> a -> Bool

and not
f :: Eq [a] => [a] -> a -> Bool

Even though the equality is taken at the list type, the context must be simpliﬁed, using the instance declaration for Eq on lists, before generalization. If no such instance is in scope, a static error occurs. Here is an example that shows the need for a constraint of the form C (m t) where m is one of the type variables being generalized; that is, where the class C applies to a type expression that is not a type variable or a type constructor. Consider:
f :: (Monad m, Eq (m a)) => a -> m a -> Bool f x y = return x == y

The type of return is Monad m => a -> m a; the type of (==) is Eq a => a -> a -> Bool. The type of f should be therefore (Monad m, Eq (m a)) => a -> m a -> Bool, and the context cannot be simpliﬁed further. The instance declaration derived from a data type deriving clause (see Section 4.3.3) must, like any instance declaration, have a simple context; that is, all the constraints must be of the form C a, where a is a type variable. For example, in the type
data Apply a b = App (a b) deriving Show

the derived Show instance will produce a context Show (a b), which cannot be reduced and is not simple; thus a static error results.

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4.5.4

Monomorphism

Sometimes it is not possible to generalize over all the type variables used in the type of the deﬁnition. For example, consider the declaration
f x = let g y z = ([x,y], z) in ...

In an environment where x has type a, the type of g’s deﬁnition is a → b → ([a], b). The generalization step attributes to g the type ∀ b. a → b → ([a], b); only b can be universally quantiﬁed because a occurs in the type environment. We say that the type of g is monomorphic in the type variable a. The effect of such monomorphism is that the ﬁrst argument of all applications of g must be of a single type. For example, it would be valid for the “...” to be
(g True, g False)

(which would, incidentally, force x to have type Bool) but invalid for it to be
(g True, g ’c’)

In general, a type ∀ u. cx ⇒ t is said to be monomorphic in the type variable a if a is free in ∀ u. cx ⇒ t. It is worth noting that the explicit type signatures provided by Haskell are not powerful enough to express types that include monomorphic type variables. For example, we cannot write
f x = let g :: a -> b -> ([a],b) g y z = ([x,y], z) in ...

because that would claim that g was polymorphic in both a and b (Section 4.4.1). In this program, g can only be given a type signature if its ﬁrst argument is restricted to a type not involving type variables; for example
g :: Int -> b -> ([Int],b)

This signature would also cause x to have type Int.

4.5.5

The Monomorphism Restriction

Haskell places certain extra restrictions on the generalization step, beyond the standard Hindley-Milner restriction described above, which further reduces polymorphism in particular cases. The monomorphism restriction depends on the binding syntax of a variable. Recall that a variable is bound by either a function binding or a pattern binding, and that a simple pattern binding is a pattern binding in which the pattern consists of only a single variable (Section 4.4.3). The following two rules deﬁne the monomorphism restriction:

4.5. STATIC SEMANTICS OF FUNCTION AND PATTERN BINDINGS The monomorphism restriction Rule 1. We say that a given declaration group is unrestricted if and only if:

57

(a): every variable in the group is bound by a function binding or a simple pattern binding (Section 4.4.3.2), and (b): an explicit type signature is given for every variable in the group that is bound by simple pattern binding. The usual Hindley-Milner restriction on polymorphism is that only type variables that do not occur free in the environment may be generalized. In addition, the constrained type variables of a restricted declaration group may not be generalized in the generalization step for that group. (Recall that a type variable is constrained if it must belong to some type class; see Section 4.5.2.) Rule 2. Any monomorphic type variables that remain when type inference for an entire module is complete, are considered ambiguous, and are resolved to particular types using the defaulting rules (Section 4.3.4).

Motivation

Rule 1 is required for two reasons, both of which are fairly subtle.

• Rule 1 prevents computations from being unexpectedly repeated. For example, genericLength is a standard function (in library Data.List) whose type is given by
genericLength :: Num a => [b] -> a

It looks as if len should be computed only once, but without Rule 1 it might be computed twice, once at each of two different overloadings. If the programmer does actually wish the computation to be repeated, an explicit type signature may be added:
let { len :: Num a => a; len = genericLength xs } in (len, len)

Recall that reads is a standard function whose type is given by the signature
reads :: (Read a) => String -> [(a,String)]

Without Rule 1, n would be assigned the type ∀ a. Read a ⇒ a and s the type ∀ a. Read a ⇒ String. The latter is an invalid type, because it is inherently ambiguous. It is not possible to determine at what overloading to use s, nor can this be solved by adding a type signature for s. Hence, when non-simple pattern bindings are used (Section 4.4.3.2), the types inferred are always monomorphic in their constrained type variables, irrespective of whether a type signature is provided. In this case, both n and s are monomorphic in a. The same constraint applies to pattern-bound functions. For example, in
(f,g) = ((+),(-))

both f and g are monomorphic regardless of any type signatures supplied for f or g. Rule 2 is required because there is no way to enforce monomorphic use of an exported binding, except by performing type inference on modules outside the current module. Rule 2 states that the exact types of all the variables bound in a module must be determined by that module alone, and not by any modules that import it.

When type inference on module M1 is complete, len1 has the monomorphic type Num a => a (by Rule 1). Rule 2 now states that the monomorphic type variable a is ambiguous, and must be resolved using the defaulting rules of Section 4.3.4. Hence, len1 gets type Int, and its use in len2 is type-incorrect. (If the above code is actually what is wanted, a type signature on len1 would solve the problem.) This issue does not arise for nested bindings, because their entire scope is visible to the compiler.

Consequences The monomorphism rule has a number of consequences for the programmer. Anything deﬁned with function syntax usually generalizes as a function is expected to. Thus in
f x y = x+y

the function f may be used at any overloading in class Num. There is no danger of recomputation here. However, the same function deﬁned with pattern syntax:
f = \x -> \y -> x+y

requires a type signature if f is to be fully overloaded. Many functions are most naturally deﬁned using simple pattern bindings; the user must be careful to afﬁx these with type signatures to retain full overloading. The standard prelude contains many examples of this:
sum sum :: (Num a) => [a] -> a = foldl (+) 0

Here, type inference ﬁnds that len1 has the monomorphic type (Num a => a); and the type variable a is resolved to Rational when performing type inference on len2.

4.6

Kind Inference

This section describes the rules that are used to perform kind inference, i.e. to calculate a suitable kind for each type constructor and class appearing in a given program. The ﬁrst step in the kind inference process is to arrange the set of datatype, synonym, and class deﬁnitions into dependency groups. This can be achieved in much the same way as the dependency analysis for value declarations that was described in Section 4.5. For example, the following program fragment includes the deﬁnition of a datatype constructor D, a synonym S and a class C, all of which would be included in the same dependency group:

The kinds of variables, constructors, and classes within each group are determined using standard techniques of type inference and kind-preserving uniﬁcation [8]. For example, in the deﬁnitions above, the parameter a appears as an argument of the function constructor (->) in the type of bar and hence must have kind ∗. It follows that both D and S must have kind ∗ → ∗ and that every instance of class C must have kind ∗. It is possible that some parts of an inferred kind may not be fully determined by the corresponding deﬁnitions; in such cases, a default of ∗ is assumed. For example, we could assume an arbitrary kind κ for the a parameter in each of the following examples:
data App f a = A (f a) data Tree a = Leaf | Fork (Tree a) (Tree a)

This would give kinds (κ → ∗) → κ → ∗ and κ → ∗ for App and Tree, respectively, for any kind κ, and would require an extension to allow polymorphic kinds. Instead, using the default binding κ = ∗, the actual kinds for these two constructors are (∗ → ∗) → ∗ → ∗ and ∗ → ∗, respectively. Defaults are applied to each dependency group without consideration of the ways in which particular type constructor constants or classes are used in later dependency groups or elsewhere in the program. For example, adding the following deﬁnition to those above does not inﬂuence the kind inferred for Tree (by changing it to (∗ → ∗) → ∗, for instance), and instead generates a static error because the kind of [], ∗ → ∗, does not match the kind ∗ that is expected for an argument of Tree:
type FunnyTree = Tree [] -- invalid

This is important because it ensures that each constructor and class are used consistently with the same kind whenever they are in scope.

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Chapter 5

Modules
A module deﬁnes a collection of values, datatypes, type synonyms, classes, etc. (see Chapter 4), in an environment created by a set of imports (resources brought into scope from other modules). It exports some of these resources, making them available to other modules. We use the term entity to refer to a value, type, or class deﬁned in, imported into, or perhaps exported from a module. A Haskell program is a collection of modules, one of which, by convention, must be called Main and must export the value main. The value of the program is the value of the identiﬁer main in module Main, which must be a computation of type IO τ for some type τ (see Chapter 7). When the program is executed, the computation main is performed, and its result (of type τ ) is discarded. Modules may reference other modules via explicit import declarations, each giving the name of a module to be imported and specifying its entities to be imported. Modules may be mutually recursive. Modules are used for name-space control, and are not ﬁrst class values. A multi-module Haskell program can be converted into a single-module program by giving each entity a unique name, changing all occurrences to refer to the appropriate unique name, and then concatenating all the module bodies1 . For example, here is a three-module program:
module Main where import A import B main = A.f >> B.f module A where f = ... module B where f = ...

It is equivalent to the following single-module program:
module Main where main = af >> bf
1 There are two minor exceptions to this statement. First, default declarations scope over a single module (Section 4.3.4). Second, Rule 2 of the monomorphism restriction (Section 4.5.5) is affected by module boundaries.

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af = ... bf = ...

Because they are allowed to be mutually recursive, modules allow a program to be partitioned freely without regard to dependencies. A module name (lexeme modid ) is a sequence of one or more identiﬁers beginning with capital letters, separated by dots, with no intervening spaces. For example, Data.Bool, Main and Foreign.Marshal.Alloc are all valid module names. modid → {conid .} conid (modules)

Module names can be thought of as being arranged in a hierarchy in which appending a new component creates a child of the original module name. For example, the module Control.Monad.ST is a child of the Control.Monad sub-hierarchy. This is purely a convention, however, and not part of the language deﬁnition; in this report a modid is treated as a single identiﬁer occupying a ﬂat namespace. There is one distinguished module, Prelude, which is imported into all modules by default (see Section 5.6), plus a set of standard library modules that may be imported as required (see Part II).

A module begins with a header: the keyword module, the module name, and a list of entities (enclosed in round parentheses) to be exported. The header is followed by a possibly-empty list of import declarations (impdecls, Section 5.3) that specify modules to be imported, optionally restricting the imported bindings. This is followed by a possibly-empty list of top-level declarations (topdecls, Chapter 4). An abbreviated form of module, consisting only of the module body, is permitted. If this is used, the header is assumed to be ‘module Main(main) where’. If the ﬁrst lexeme in the abbreviated module is not a {, then the layout rule applies for the top level of the module.

An export list identiﬁes the entities to be exported by a module declaration. A module implementation may only export an entity that it declares, or that it imports from some other module. If the export list is omitted, all values, types and classes deﬁned in the module are exported, but not those that are imported. Entities in an export list may be named as follows: 1. A value, ﬁeld name, or class method, whether declared in the module body or imported, may be named by giving the name of the value as a qvarid , which must be in scope. Operators should be enclosed in parentheses to turn them into qvarid s. 2. An algebraic datatype T declared by a data or newtype declaration may be named in one of three ways: • The form T names the type but not the constructors or ﬁeld names. The ability to export a type without its constructors allows the construction of abstract datatypes (see Section 5.8). • The form T (c1 , . . . ,cn ), names the type and some or all of its constructors and ﬁeld names. • The abbreviated form T (..) names the type and all its constructors and ﬁeld names that are currently in scope (whether qualiﬁed or not). In all cases, the (possibly-qualiﬁed) type constructor T must be in scope. The constructor and ﬁeld names ci in the second form are unqualiﬁed; one of these subordinate names is legal if and only if (a) it names a constructor or ﬁeld of T , and (b) the constructor or ﬁeld is in scope in the module body regardless of whether it is in scope under a qualiﬁed or unqualiﬁed name. For example, the following is legal
module A( Mb.Maybe( Nothing, Just ) ) where import qualified Data.Maybe as Mb

Data constructors cannot be named in export lists except as subordinate names, because they cannot otherwise be distinguished from type constructors. 3. A type synonym T declared by a type declaration may be named by the form T , where T is in scope. 4. A class C with operations f1 , . . . , fn declared in a class declaration may be named in one of three ways: • The form C names the class but not the class methods. • The form C(f1 , . . . ,fn ), names the class and some or all of its methods. • The abbreviated form C(..) names the class and all its methods that are in scope (whether qualiﬁed or not).

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CHAPTER 5. MODULES In all cases, C must be in scope. In the second form, one of the (unqualiﬁed) subordinate names fi is legal if and only if (a) it names a class method of C , and (b) the class method is in scope in the module body regardless of whether it is in scope under a qualiﬁed or unqualiﬁed name. 5. The form “module M” names the set of all entities that are in scope with both an unqualiﬁed name “e” and a qualiﬁed name “M.e”. This set may be empty. For example:
module Queue( module Stack, enqueue, dequeue ) where import Stack ...

Here the module Queue uses the module name Stack in its export list to abbreviate all the entities imported from Stack. A module can name its own local deﬁnitions in its export list using its own name in the “module M” syntax, because a local declaration brings into scope both a qualiﬁed and unqualiﬁed name (Section 5.5.1). For example:
module Mod1( module Mod1, module Mod2 ) where import Mod2 import Mod3

Here module Mod1 exports all local deﬁnitions as well as those imported from Mod2 but not those imported from Mod3. It is an error to use module M in an export list unless M is the module bearing the export list, or M is imported by at least one import declaration (qualiﬁed or unqualiﬁed). Exports lists are cumulative: the set of entities exported by an export list is the union of the entities exported by the individual items of the list. It makes no difference to an importing module how an entity was exported. For example, a ﬁeld name f from data type T may be exported individually (f, item (1) above); or as an explicitly-named member of its data type (T(f), item (2)); or as an implicitly-named member (T(..), item(2)); or by exporting an entire module (module M, item (5)). The unqualiﬁed names of the entities exported by a module must all be distinct (within their respective namespace). For example
module A ( C.f, C.g, g, module B ) where import B(f) import qualified C(f,g) g = f True -- an invalid module

There are no name clashes within module A itself, but there are name clashes in the export list between C.g and g (assuming C.g and g are different entities – remember, modules can import each other recursively), and between module B and C.f (assuming B.f and C.f are different entities).

The entities exported by a module may be brought into scope in another module with an import declaration at the beginning of the module. The import declaration names the module to be imported and optionally speciﬁes the entities to be imported. A single module may be imported by more than one import declaration. Imported names serve as top level declarations: they scope over the entire body of the module but may be shadowed by local non-top-level bindings. The effect of multiple import declarations is strictly cumulative: an entity is in scope if it is imported by any of the import declarations in a module. The ordering of import declarations is irrelevant. Lexically, the terminal symbols “as”, “qualified” and “hiding” are each a varid rather than a reservedid . They have special signiﬁcance only in the context of an import declaration; they may also be used as variables.

5.3.1

What is imported

Exactly which entities are to be imported can be speciﬁed in one of the following three ways: 1. The imported entities can be speciﬁed explicitly by listing them in parentheses. Items in the list have the same form as those in export lists, except qualiﬁers are not permitted and the ‘module modid ’ entity is not permitted. When the (..) form of import is used for a type or class, the (..) refers to all of the constructors, methods, or ﬁeld names exported from the module. The list must name only entities exported by the imported module. The list may be empty, in which case nothing except the instances is imported. 2. Entities can be excluded by using the form hiding(import1 , . . . , importn ), which speciﬁes that all entities exported by the named module should be imported except for those named in the list. Data constructors may be named directly in hiding lists without being preﬁxed by the associated type. Thus, in
import M hiding (C)

any constructor, class, or type named C is excluded. In contrast, using C in an import list names only a class or type. It is an error to hide an entity that is not, in fact, exported by the imported module. 3. Finally, if impspec is omitted then all the entities exported by the speciﬁed module are imported.

5.3.2

Qualiﬁed import

For each entity imported under the rules of Section 5.3.1, the top-level environment is extended. If the import declaration used the qualified keyword, only the qualiﬁed name of the entity is brought into scope. If the qualified keyword is omitted, then both the qualiﬁed and unqualiﬁed name of the entity is brought into scope. Section 5.5.1 describes qualiﬁed names in more detail.

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The qualiﬁer on the imported name is either the name of the imported module, or the local alias given in the as clause (Section 5.3.3) on the import statement. Hence, the qualiﬁer is not necessarily the name of the module in which the entity was originally declared. The ability to exclude the unqualiﬁed names allows full programmer control of the unqualiﬁed namespace: a locally deﬁned entity can share the same name as a qualiﬁed import:
module Ring where import qualified Prelude import Data.List( nub ) l1 + l2 = l1 Prelude.++ l2 l1 * l2 = nub (l1 + l2) succ = (Prelude.+ 1)

-- All Prelude names must be qualified

-- This + differs from the one in the Prelude -- This * differs from the one in the Prelude

5.3.3

Local aliases

Imported modules may be assigned a local alias in the importing module using the as clause. For example, in
import qualified VeryLongModuleName as C

entities must be referenced using ‘C.’ as a qualiﬁer instead of ‘VeryLongModuleName.’. This also allows a different module to be substituted for VeryLongModuleName without changing the qualiﬁers used for the imported module. It is legal for more than one module in scope to use the same qualiﬁer, provided that all names can still be resolved unambiguously. For example:
module M where import qualified Foo as A import qualified Baz as A x = A.f

This module is legal provided only that Foo and Baz do not both export f. An as clause may also be used on an un-qualified import statement:
import Foo as A(f)

This declaration brings into scope f and A.f.

5.3.4

Examples

To clarify the above import rules, suppose the module A exports x and y. Then this table shows what names are brought into scope by the speciﬁed import statement:

In all cases, all instance declarations in scope in module A are imported (Section 5.4).

5.4

Importing and Exporting Instance Declarations

Instance declarations cannot be explicitly named on import or export lists. All instances in scope within a module are always exported and any import brings all instances in from the imported module. Thus, an instance declaration is in scope if and only if a chain of import declarations leads to the module containing the instance declaration. For example, import M() does not bring any new names in scope from module M, but does bring in any instances visible in M. A module whose only purpose is to provide instance declarations can have an empty export list. For example
module MyInstances() where instance Show (a -> b) where show fn = "<<function>>" instance Show (IO a) where show io = "<<IO action>>"

5.5
5.5.1

Name Clashes and Closure
Qualiﬁed names

A qualiﬁed name is written as modid .name (Section 2.4). A qualiﬁed name is brought into scope: • By a top level declaration. A top-level declaration brings into scope both the unqualiﬁed and the qualiﬁed name of the entity being deﬁned. Thus:
module M where f x = ... g x = M.f x x

• By an import declaration. An import declaration, whether qualified or not, always brings into scope the qualiﬁed name of the imported entity (Section 5.3). This allows a qualiﬁed import to be replaced with an unqualiﬁed one without forcing changes in the references to the imported names.

5.5.2

Name clashes

If a module contains a bound occurrence of a name, such as f or A.f, it must be possible unambiguously to resolve which entity is thereby referred to; that is, there must be only one binding for f or A.f respectively. It is not an error for there to exist names that cannot be so resolved, provided that the program does not mention those names. For example:
module A where import B import C tup = (b, c, d, x) module B( d, b, x, y ) where import D x = ... y = ... b = ... module C( d, c, x, y ) where import D x = ... y = ... c = ... module D( d ) where d = ...

Consider the deﬁnition of tup. • The references to b and c can be unambiguously resolved to b declared in B, and c declared in C respectively. • The reference to d is unambiguously resolved to d declared in D. In this case the same entity is brought into scope by two routes (the import of B and the import of C), and can be referred to in A by the names d, B.d, and C.d. • The reference to x is ambiguous: it could mean x declared in B, or x declared in C. The ambiguity could be ﬁxed by replacing the reference to x by B.x or C.x. • There is no reference to y, so it is not erroneous that distinct entities called y are exported by both B and C. An error is only reported if y is actually mentioned.

5.5. NAME CLASHES AND CLOSURE

69

The name occurring in a type signature or ﬁxity declarations is always unqualiﬁed, and unambiguously refers to another declaration in the same declaration list (except that the ﬁxity declaration for a class method can occur at top level — Section 4.4.2). For example, the following module is legal:
module F where sin :: Float -> Float sin x = (x::Float) f x = Prelude.sin (F.sin x)

The local declaration for sin is legal, even though the Prelude function sin is implicitly in scope. The references to Prelude.sin and F.sin must both be qualiﬁed to make it unambiguous which sin is meant. However, the unqualiﬁed name sin in the type signature in the ﬁrst line of F unambiguously refers to the local declaration for sin.

5.5.3

Closure

Every module in a Haskell program must be closed. That is, every name explicitly mentioned by the source code must be either deﬁned locally or imported from another module. However, entities that the compiler requires for type checking or other compile time analysis need not be imported if they are not mentioned by name. The Haskell compilation system is responsible for ﬁnding any information needed for compilation without the help of the programmer. That is, the import of a variable x does not require that the datatypes and classes in the signature of x be brought into the module along with x unless these entities are referenced by name in the user program. The Haskell system silently imports any information that must accompany an entity for type checking or any other purposes. Such entities need not even be explicitly exported: the following program is valid even though T does not escape M1:
module M1(x) where data T = T x = T module M2 where import M1(x) y = x

In this example, there is no way to supply an explicit type signature for y since T is not in scope. Whether or not T is explicitly exported, module M2 knows enough about T to correctly type check the program. The type of an exported entity is unaffected by non-exported type synonyms. For example, in
module M(x) where type T = Int x :: T x = 1

the type of x is both T and Int; these are interchangeable even when T is not in scope. That is, the deﬁnition of T is available to any module that encounters it whether or not the name T is in scope. The only reason to export T is to allow other modules to refer it by name; the type checker ﬁnds the deﬁnition of T if needed whether or not it is exported.

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5.6

Standard Prelude

Many of the features of Haskell are deﬁned in Haskell itself as a library of standard datatypes, classes, and functions, called the “Standard Prelude.” In Haskell, the Prelude is contained in the module Prelude. There are also many predeﬁned library modules, which provide less frequently used functions and types. For example, complex numbers, arrays, and most of the input/output are all part of the standard libraries. These are deﬁned in Part II. Separating libraries from the Prelude has the advantage of reducing the size and complexity of the Prelude, allowing it to be more easily assimilated, and increasing the space of useful names available to the programmer. Prelude and library modules differ from other modules in that their semantics (but not their implementation) are a ﬁxed part of the Haskell language deﬁnition. This means, for example, that a compiler may optimize calls to functions in the Prelude without consulting the source code of the Prelude.

5.6.1

The Prelude Module

The Prelude module is imported automatically into all modules as if by the statement ‘import Prelude’, if and only if it is not imported with an explicit import declaration. This provision for explicit import allows entities deﬁned in the Prelude to be selectively imported, just like those from any other module. The semantics of the entities in Prelude is speciﬁed by a reference implementation of Prelude written in Haskell, given in Chapter 9. Some datatypes (such as Int) and functions (such as Int addition) cannot be speciﬁed directly in Haskell. Since the treatment of such entities depends on the implementation, they are not formally deﬁned in Chapter 9. The implementation of Prelude is also incomplete in its treatment of tuples: there should be an inﬁnite family of tuples and their instance declarations, but the implementation only gives a scheme. Chapter 9 deﬁnes the module Prelude using several other modules: PreludeList, PreludeIO, and so on. These modules are not part of Haskell 98, and they cannot be imported separately. They are simply there to help explain the structure of the Prelude module; they should be considered part of its implementation, not part of the language deﬁnition.

5.6.2

Shadowing Prelude Names

The rules about the Prelude have been cast so that it is possible to use Prelude names for nonstandard purposes; however, every module that does so must have an import declaration that makes this nonstandard usage explicit. For example:
module A( null, nonNull ) where import Prelude hiding( null ) null, nonNull :: Int -> Bool null x = x == 0 nonNull x = not (null x)

Module A redeﬁnes null, and contains an unqualiﬁed reference to null on the right hand side of nonNull. The latter would be ambiguous without the hiding(null) on the import Prelude statement. Every module that imports A unqualiﬁed, and then makes an unqualiﬁed reference to null must also resolve the ambiguous use of null just as A does. Thus there is little danger of accidentally shadowing Prelude names.

5.7. SEPARATE COMPILATION

71

It is possible to construct and use a different module to serve in place of the Prelude. Other than the fact that it is implicitly imported, the Prelude is an ordinary Haskell module; it is special only in that some objects in the Prelude are referenced by special syntactic constructs. Redeﬁning names used by the Prelude does not affect the meaning of these special constructs. For example, in
module B where import Prelude() import MyPrelude f x = (x,x) g x = (,) x x h x = [x] ++ []

the explicit import Prelude() declaration prevents the automatic import of Prelude, while the declaration import MyPrelude brings the non-standard prelude into scope. The special syntax for tuples (such as (x,x) and (,)) and lists (such as [x] and []) continues to refer to the tuples and lists deﬁned by the standard Prelude; there is no way to redeﬁne the meaning of [x], for example, in terms of a different implementation of lists. On the other hand, the use of ++ is not special syntax, so it refers to ++ imported from MyPrelude. It is not possible, however, to hide instance declarations in the Prelude. For example, one cannot deﬁne a new instance for Show Char.

5.7

Separate Compilation

Depending on the Haskell implementation used, separate compilation of mutually recursive modules may require that imported modules contain additional information so that they may be referenced before they are compiled. Explicit type signatures for all exported values may be necessary to deal with mutual recursion. The precise details of separate compilation are not deﬁned by this report.

Modules importing Stack cannot construct values of type StkType because they do not have access to the constructors of the type. Instead, they must use push, pop, and empty to construct such values. It is also possible to build an ADT on top of an existing type by using a newtype declaration. For example, stacks can be deﬁned with lists:
module Stack( StkType, push, pop, empty ) where newtype StkType a = Stk [a] push x (Stk s) = Stk (x:s) pop (Stk (_:s)) = Stk s empty = Stk []

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Chapter 6

Predeﬁned Types and Classes
The Haskell Prelude contains predeﬁned classes, types, and functions that are implicitly imported into every Haskell program. In this chapter, we describe the types and classes found in the Prelude. Most functions are not described in detail here as they can easily be understood from their deﬁnitions as given in Chapter 9. Other predeﬁned types such as arrays, complex numbers, and rationals are deﬁned in Part II.

6.1

Standard Haskell Types

These types are deﬁned by the Haskell Prelude. Numeric types are described in Section 6.4. When appropriate, the Haskell deﬁnition of the type is given. Some deﬁnitions may not be completely valid on syntactic grounds but they faithfully convey the meaning of the underlying type.

The boolean type Bool is an enumeration. The basic boolean functions are && (and), || (or), and not. The name otherwise is deﬁned as True to make guarded expressions more readable.

6.1.2

Characters and Strings

The character type Char is an enumeration whose values represent Unicode characters [2]. The lexical syntax for characters is deﬁned in Section 2.6; character literals are nullary constructors in the datatype Char. Type Char is an instance of the classes Read, Show, Eq, Ord, Enum, and Bounded. The toEnum and fromEnum functions, standard functions from class Enum, map characters to and from the Int type. Note that ASCII control characters each have several representations in character literals: numeric escapes, ASCII mnemonic escapes, and the \ˆX notation. In addition, there are the following equivalences: \a and \BEL, \b and \BS, \f and \FF, \r and \CR, \t and \HT, \v and \VT, and \n and \LF. A string is a list of characters: 73

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type String = [Char]

CHAPTER 6. PREDEFINED TYPES AND CLASSES

Strings may be abbreviated using the lexical syntax described in Section 2.6. For example, "A string" abbreviates [ ’A’,’ ’,’s’,’t’,’r’, ’i’,’n’,’g’]

6.1.3

Lists
data [a] = [] | a : [a] deriving (Eq, Ord)

Lists are an algebraic datatype of two constructors, although with special syntax, as described in Section 3.7. The ﬁrst constructor is the null list, written ‘[]’ (“nil”), and the second is ‘:’ (“cons”). The module PreludeList (see Section 9.1) deﬁnes many standard list functions. Arithmetic sequences and list comprehensions, two convenient syntaxes for special kinds of lists, are described in Sections 3.10 and 3.11, respectively. Lists are an instance of classes Read, Show, Eq, Ord, Monad, Functor, and MonadPlus.

6.1.4

Tuples

Tuples are algebraic datatypes with special syntax, as deﬁned in Section 3.8. Each tuple type has a single constructor. All tuples are instances of Eq, Ord, Bounded, Read, and Show (provided, of course, that all their component types are). There is no upper bound on the size of a tuple, but some Haskell implementations may restrict the size of tuples, and limit the instances associated with larger tuples. However, every Haskell implementation must support tuples up to size 15, together with the instances for Eq, Ord, Bounded, Read, and Show. The Prelude and libraries deﬁne tuple functions such as zip for tuples up to a size of 7. The constructor for a tuple is written by omitting the expressions surrounding the commas; thus (x,y) and (,) x y produce the same value. The same holds for tuple type constructors; thus, (Int,Bool,Int) and (,,) Int Bool Int denote the same type. The following functions are deﬁned for pairs (2-tuples): fst, snd, curry, and uncurry. Similar functions are not predeﬁned for larger tuples.

The unit datatype () has one non-⊥ member, the nullary constructor (). See also Section 3.9.

6.1.6

Function Types

Functions are an abstract type: no constructors directly create functional values. The following simple functions are found in the Prelude: id, const, (.), flip, ($), and until.

6.2. STRICT EVALUATION

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6.1.7

The IO and IOError Types

The IO type serves as a tag for operations (actions) that interact with the outside world. The IO type is abstract: no constructors are visible to the user. IO is an instance of the Monad and Functor classes. Chapter 7 describes I/O operations. IOError is an abstract type representing errors raised by I/O operations. It is an instance of Show and Eq. Values of this type are constructed by the various I/O functions and are not presented in any further detail in this report. The Prelude contains a few I/O functions (deﬁned in Section 9.3), and Part II contains many more.

The Maybe type is an instance of classes Functor, Monad, and MonadPlus. The Ordering type is used by compare in the class Ord. The functions maybe and either are found in the Prelude.

6.2

Strict Evaluation

Function application in Haskell is non-strict; that is, a function argument is evaluated only when required. Sometimes it is desirable to force the evaluation of a value, using the seq function:
seq :: a -> b -> b

The function seq is deﬁned by the equations: seq ⊥ b = ⊥ seq a b = b, if a = ⊥ seq is usually introduced to improve performance by avoiding unneeded laziness. Strict datatypes (see Section 4.2.1) are deﬁned in terms of the $! operator. However, the provision of seq has important semantic consequences, because it is available at every type. As a consequence, ⊥ is not the same as \x -> ⊥, since seq can be used to distinguish them. For the same reason, the existence of seq weakens Haskell’s parametricity properties. The operator $! is strict (call-by-value) application, and is deﬁned in terms of seq. The Prelude also deﬁnes the $ operator to perform non-strict application.
infixr 0 $, $! ($), ($!) :: (a -> b) -> a -> b f $ x = f x f $! x = x ‘seq‘ f x

The non-strict application operator $ may appear redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

76

CHAPTER 6. PREDEFINED TYPES AND CLASSES

Eq
All except IO, (->)

Show
All except IO, (->)

Read
All except IO, (->)

Ord
All except (->) IO, IOError

Num
Int, Integer, Float, Double

Bounded
Int, Char, Bool, () Ordering, tuples

Enum
(), Bool, Char, Ordering, Int, Integer, Float, Double

Real
Int, Integer, Float, Double

Fractional
Float, Double

Integral
Int, Integer

RealFrac
Float, Double

Floating
Float, Double

RealFloat
Float, Double

Monad
IO, [], Maybe

Functor
IO, [], Maybe

Figure 6.1: Standard Haskell Classes

f $ g $ h x

=

f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

6.3

Standard Haskell Classes

Figure 6.1 shows the hierarchy of Haskell classes deﬁned in the Prelude and the Prelude types that are instances of these classes. Default class method declarations (Section 4.3) are provided for many of the methods in standard classes. A comment with each class declaration in Chapter 9 speciﬁes the smallest collection of method deﬁnitions that, together with the default declarations, provide a reasonable deﬁnition for all the class methods. If there is no such comment, then all class methods must be given to fully specify an instance.

The Eq class provides equality (==) and inequality (/=) methods. All basic datatypes except for functions and IO are instances of this class. Instances of Eq can be derived for any user-deﬁned datatype whose constituents are also instances of Eq. This declaration gives default method declarations for both /= and ==, each being deﬁned in terms of the other. If an instance declaration for Eq deﬁnes neither == nor /=, then both will loop. If one is deﬁned, the default method for the other will make use of the one that is deﬁned. If both are deﬁned, neither default method is used.

The Ord class is used for totally ordered datatypes. All basic datatypes except for functions, IO, and IOError, are instances of this class. Instances of Ord can be derived for any user-deﬁned datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects. The default declarations allow a user to create an Ord instance either with a type-speciﬁc compare function or with type-speciﬁc == and <= functions.

The Read and Show classes are used to convert values to or from strings. The Int argument to showsPrec and readsPrec gives the operator precedence of the enclosing context (see Section 11.4). showsPrec and showList return a String-to-String function, to allow constant-time concatenation of its results using function composition. A specialised variant, show, is also provided, which uses precedence context zero, and returns an ordinary String. The method showList is provided to allow the programmer to give a specialised way of showing lists of values. This is particularly useful for the Char type, where values of type String should be shown in double quotes, rather than between square brackets. Derived instances of Read and Show replicate the style in which a constructor is declared: inﬁx constructors and ﬁeld names are used on input and output. Strings produced by showsPrec are usually readable by readsPrec. All Prelude types, except function types and IO types, are instances of Show and Read. (If desired, a programmer can easily make functions and IO types into (vacuous) instances of Show, by providing an instance declaration.) For convenience, the Prelude provides the following auxiliary functions:
reads reads shows shows read read s :: (Read a) => ReadS a = readsPrec 0 :: (Show a) => a -> ShowS = showsPrec 0 :: (Read a) => String -> a = case [x | (x,t) <- reads s, ("","") <- lex t] of [x] -> x [] -> error "PreludeText.read: no parse" _ -> error "PreludeText.read: ambiguous parse"

shows and reads use a default precedence of 0. The read function reads input from a string, which must be completely consumed by the input process. The function lex :: ReadS String, used by read, is also part of the Prelude. It reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful “lexeme” consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, lex fails (i.e. returns []).

Class Enum deﬁnes operations on sequentially ordered types. The functions succ and pred return the successor and predecessor, respectively, of a value. The functions fromEnum and toEnum map values from a type in Enum to and from Int. The enumFrom... methods are used when translating arithmetic sequences (Section 3.10). Instances of Enum may be derived for any enumeration type (types whose constructors have no ﬁelds); see Chapter 11. For any type that is an instance of class Bounded as well as Enum, the following should hold: • The calls succ maxBound and pred minBound should result in a runtime error. • fromEnum and toEnum should give a runtime error if the result value is not representable in the result type. For example, toEnum 7 :: Bool is an error. • enumFrom and enumFromThen should be deﬁned with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound enumFromThen x y = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = maxBound | otherwise = minBound

The following Prelude types are instances of Enum: • Enumeration types: (), Bool, and Ordering. The semantics of these instances is given by Chapter 11. For example, [LT..] is the list [LT,EQ,GT]. • Char: the instance is given in Chapter 9, based on the primitive functions that convert between a Char and an Int. For example, enumFromTo ’a’ ’z’ denotes the list of lowercase letters in alphabetical order. • Numeric types: Int, Integer, Float, Double. The semantics of these instances is given next. For all four numeric types, succ adds 1, and pred subtracts 1. The conversions fromEnum and toEnum convert between the type and Int. In the case of Float and Double, the digits after the decimal point may be lost. It is implementation-dependent what fromEnum returns when applied to a value that is too large to ﬁt in an Int. For the types Int and Integer, the enumeration functions have the following meaning:

80

CHAPTER 6. PREDEFINED TYPES AND CLASSES • The sequence enumFrom e1 is the list [e1 ,e1 + 1 ,e1 + 2 , . . . ]. • The sequence enumFromThen e1 e2 is the list [e1 ,e1 + i ,e1 + 2i , . . . ], where the increment, i , is e2 − e1 . The increment may be zero or negative. If the increment is zero, all the list elements are the same. • The sequence enumFromTo e1 e3 is the list [e1 ,e1 + 1 ,e1 + 2 , . . . e3 ]. The list is empty if e1 > e3 . • The sequence enumFromThenTo e1 e2 e3 is the list [e1 ,e1 + i ,e1 + 2i , . . . e3 ], where the increment, i , is e2 − e1 . If the increment is positive or zero, the list terminates when the next element would be greater than e3 ; the list is empty if e1 > e3 . If the increment is negative, the list terminates when the next element would be less than e3 ; the list is empty if e1 < e3 .

For Float and Double, the semantics of the enumFrom family is given by the rules for Int above, except that the list terminates when the elements become greater than e3 + i /2 for positive increment i , or when they become less than e3 + i /2 for negative i . For all four of these Prelude numeric types, all of the enumFrom family of functions are strict in all their arguments.

The Monad class deﬁnes the basic operations over a monad. See Chapter 7 for more information about monads. “do” expressions provide a convenient syntax for writing monadic expressions (see Section 3.14). The fail method is invoked on pattern-match failure in a do expression.

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds. The types Int, Char, Bool, (), Ordering, and all tuples are instances of Bounded. The Bounded class may be derived for any enumeration type; minBound is the ﬁrst constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

6.4

Numbers

Haskell provides several kinds of numbers; the numeric types and the operations upon them have been heavily inﬂuenced by Common Lisp and Scheme. Numeric function names and operators are usually overloaded, using several type classes with an inclusion relation shown in Figure 6.1. The class Num of numeric types is a subclass of Eq, since all numbers may be compared for equality; its subclass Real is also a subclass of Ord, since the other comparison operations apply to all but complex numbers (deﬁned in the Complex library). The class Integral contains integers of both limited and unlimited range; the class Fractional contains all non-integral types; and the class Floating contains all ﬂoating-point types, both real and complex. The Prelude deﬁnes only the most basic numeric types: ﬁxed sized integers (Int), arbitrary precision integers (Integer), single precision ﬂoating (Float), and double precision ﬂoating (Double). Other numeric types such as rationals and complex numbers are deﬁned in libraries. In particular, the type Rational is a ratio of two Integer values, as deﬁned in the Ratio library.

The default ﬂoating point operations deﬁned by the Haskell Prelude do not conform to current language independent arithmetic (LIA) standards. These standards require considerably more complexity in the numeric structure and have thus been relegated to a library. Some, but not all, aspects of the IEEE ﬂoating point standard have been accounted for in Prelude class RealFloat. The standard numeric types are listed in Table 6.1. The ﬁnite-precision integer type Int covers at least the range [ − 2 29 , 2 29 − 1 ]. As Int is an instance of the Bounded class, maxBound and minBound can be used to determine the exact Int range deﬁned by an implementation. Float is implementationdeﬁned; it is desirable that this type be at least equal in range and precision to the IEEE single-precision type. Similarly, Double should cover IEEE double-precision. The results of exceptional conditions (such as overﬂow or underﬂow) on the ﬁxed-precision numeric types are undeﬁned; an implementation may choose error (⊥, semantically), a truncated value, or a special value such as inﬁnity, indeﬁnite, etc. The standard numeric classes and other numeric functions deﬁned in the Prelude are shown in Figures 6.2– 6.3. Figure 6.1 shows the class dependencies and built-in types that are instances of the numeric classes.

6.4.1

Numeric Literals

The syntax of numeric literals is given in Section 2.5. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer. Similarly, a ﬂoating literal stands for an application of fromRational to a value of type Rational (that is, Ratio Integer). Given the typings:
fromInteger :: (Num a) => Integer -> a fromRational :: (Fractional a) => Rational -> a

integer and ﬂoating literals have the typings (Num a) => a and (Fractional a) => a, respectively. Numeric literals are deﬁned in this indirect way so that they may be interpreted as values of any appropriate numeric type. See Section 4.3.4 for a discussion of overloading ambiguity.

6.4.2

Arithmetic and Number-Theoretic Operations

The inﬁx class methods (+), (*), (-), and the unary function negate (which can also be written as a preﬁx minus sign; see section 3.4) apply to all numbers. The class methods quot, rem, div, and mod apply only to integral numbers, while the class method (/) applies only to fractional ones. The quot, rem, div, and mod class methods satisfy these laws if y is non-zero:

The one-argument exponential function exp and the logarithm function log act on ﬂoating-point numbers and use base e. logBase a x returns the logarithm of x in base a. sqrt returns the principal square root of a ﬂoating-point number. There are three two-argument exponentiation operations: (ˆ) raises any number to a nonnegative integer power, (ˆˆ) raises a fractional number to any integer power, and (**) takes two ﬂoating-point arguments. The value of x ˆ0 or x ˆˆ0 is 1 for any x , including zero; 0**y is undeﬁned.

6.4.4

Magnitude and Sign

A number has a magnitude and a sign. The functions abs and signum apply to any number and satisfy the law:
abs x * signum x == x

Class Floating provides the circular and hyperbolic sine, cosine, and tangent functions and their inverses. Default implementations of tan, tanh, logBase, **, and sqrt are provided, but implementors are free to provide more accurate implementations. Class RealFloat provides a version of arctangent taking two real ﬂoating-point arguments. For real ﬂoating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x , y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default deﬁnition of atan2 is provided, but implementors can provide a more accurate implementation. The precise deﬁnition of the above functions is as in Common Lisp, which in turn follows Penﬁeld’s proposal for APL [12]. See these references for discussions of branch cuts, discontinuities, and implementation.

6.4.6

Coercions and Component Extraction

The ceiling, floor, truncate, and round functions each take a real fractional argument and return an integral result. ceiling x returns the least integer not less than x , and floor x , the greatest integer not greater than x . truncate x yields the integer nearest x between 0 and x , inclusive. round x returns the nearest integer to x , the even integer if x is equidistant between two integers. The function properFraction takes a real fractional number x and returns a pair (n, f ) such that x = n + f , and: n is an integral number with the same sign as x ; and f is a fraction f with the same type and sign as x , and with absolute value less than 1. The ceiling, floor, truncate, and round functions can be deﬁned in terms of properFraction. Two functions convert numbers to type Rational: toRational returns the rational equivalent of its real argument with full precision; approxRational takes two real fractional arguments x and and returns the simplest rational number within of x , where a rational p/q in reduced form is simpler than another p /q if |p| ≤ |p | and q ≤ q . Every real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all. The class methods of class RealFloat allow efﬁcient, machine-independent access to the components of a ﬂoating-point number. The functions floatRadix, floatDigits, and floatRange give the parameters of a ﬂoating-point type: the radix of the representation, the number of digits of this radix in the signiﬁcand, and the lowest and highest values the exponent may assume, respectively. The function decodeFloat applied to a real ﬂoating-point number returns the signiﬁcand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to mb n , where b is the ﬂoating-point radix, and furthermore, either m and n are both zero or else b d−1 ≤ m < b d , where d is the value of floatDigits x. encodeFloat performs the inverse of this transformation. The functions significand and exponent together provide the same information as decodeFloat, but rather than an Integer, significand x yields a value of the same type as x, scaled to lie in the open interval (−1 , 1 ). exponent 0 is zero. scaleFloat multiplies a ﬂoating-point number by an integer power of the radix. The functions isNaN, isInfinite, isDenormalized, isNegativeZero, and isIEEE all support numbers represented using the IEEE standard. For non-IEEE ﬂoating point numbers, these may all return false. Also available are the following coercion functions:

Basic Input/Output
The I/O system in Haskell is purely functional, yet has all of the expressive power found in conventional programming languages. To achieve this, Haskell uses a monad to integrate I/O operations into a purely functional context. The I/O monad used by Haskell mediates between the values natural to a functional language and the actions that characterize I/O operations and imperative programming in general. The order of evaluation of expressions in Haskell is constrained only by data dependencies; an implementation has a great deal of freedom in choosing this order. Actions, however, must be ordered in a well-deﬁned manner for program execution – and I/O in particular – to be meaningful. Haskell’s I/O monad provides the user with a way to specify the sequential chaining of actions, and an implementation is obliged to preserve this order. The term monad comes from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype. In the case of the I/O monad, the abstract values are the actions mentioned above. Some operations are primitive actions, corresponding to conventional I/O operations. Special operations (methods in the class Monad, see Section 6.3.6) sequentially compose actions, corresponding to sequencing operators (such as the semicolon) in imperative languages.

7.1

Standard I/O Functions

Although Haskell provides fairly sophisticated I/O facilities, as deﬁned in the IO library, it is possible to write many Haskell programs using only the few simple functions that are exported from the Prelude, and which are described in this section. All I/O functions deﬁned here are character oriented. The treatment of the newline character will vary on different systems. For example, two characters of input, return and linefeed, may read as a single newline character. These functions cannot be used portably for binary I/O. In the following, recall that String is a synonym for [Char] (Section 6.1.2).

Output Functions

These functions write to the standard output device (this is normally the user’s terminal). 87

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline. For example, a program to print the ﬁrst 20 integers and their powers of 2 could be written as:
main = print ([(n, 2ˆn) | n <- [0..19]])

Input Functions

These functions read input from the standard input device (normally the user’s terminal).

The getChar operation raises an exception (Section 7.3) on end-of-ﬁle; a predicate isEOFError that identiﬁes this exception is deﬁned in the IO library. The getLine operation raises an exception under the same circumstances as hGetLine, deﬁned the IO library. The getContents operation returns all user input as a single string, which is read lazily as it is needed. The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device. Typically, the read operation from class Read is used to convert the string to a value. The readIO function is similar to read except that it signals parse failure to the I/O monad instead of terminating the program. The readLn function combines getLine and readIO. The following program simply removes all non-ASCII characters from its standard input and echoes the result on its standard output. (The isAscii function is deﬁned in a library.)
main = interact (filter isAscii)

Files These functions operate on ﬁles of characters. Files are named by strings using some implementationspeciﬁc method to resolve strings as ﬁle names. The writeFile and appendFile functions write or append the string, their second argument, to the ﬁle, their ﬁrst argument. The readFile function reads a ﬁle and returns the contents of the ﬁle as a string. The ﬁle is read lazily, on demand, as with getContents.
type FilePath = String

Note that writeFile and appendFile write a literal string to a ﬁle. To write a value of any printable type, as with print, use the show function to convert the value to a string ﬁrst.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

7.2

Sequencing I/O Operations

The type constructor IO is an instance of the Monad class. The two monadic binding functions, methods in the Monad class, are used to compose a series of I/O operations. The >> function is used where the result of the ﬁrst operation is uninteresting, for example when it is (). The >>= operation passes the result of the ﬁrst operation as an argument to the second operation.
(>>=) :: IO a -> (a -> IO b) -> IO b (>>) :: IO a -> IO b -> IO b

is similar to the previous example using interact, but takes its input from "input-file" and writes its output to "output-file". A message is printed on the standard output before the program completes. The do notation allows programming in a more imperative syntactic style. A slightly more elaborate version of the previous example would be:
main = do putStr "Input file: " ifile <- getLine putStr "Output file: " ofile <- getLine s <- readFile ifile writeFile ofile (filter isAscii s) putStr "Filtering successful\n"

The return function is used to deﬁne the result of an I/O operation. For example, getLine is deﬁned in terms of getChar, using return to deﬁne the result:
getLine :: IO String getLine = do c <- getChar if c == ’\n’ then return "" else do s <- getLine return (c:s)

90

CHAPTER 7. BASIC INPUT/OUTPUT

7.3

Exception Handling in the I/O Monad

The I/O monad includes a simple exception handling system. Any I/O operation may raise an exception instead of returning a result. Exceptions in the I/O monad are represented by values of type IOError. This is an abstract type: its constructors are hidden from the user. The IO library deﬁnes functions that construct and examine IOError values. The only Prelude function that creates an IOError value is userError. User error values include a string describing the error.
userError :: String -> IOError

The ioError function raises an exception; the catch function establishes a handler that receives any exception raised in the action protected by catch. An exception is caught by the most recent handler established by catch. These handlers are not selective: all exceptions are caught. Exception propagation must be explicitly provided in a handler by re-raising any unwanted exceptions. For example, in
f = catch g (\e -> if IO.isEOFError e then return [] else ioError e)

the function f returns [] when an end-of-ﬁle exception occurs in g; otherwise, the exception is propagated to the next outer handler. The isEOFError function is part of IO library. When an exception propagates outside the main program, the Haskell system prints the associated IOError value and exits the program. The fail method of the IO instance of the Monad class (Section 6.3.6) raises a userError, thus:
instance Monad IO where ...bindings for return, (>>=), (>>) fail s = ioError (userError s)

The exceptions raised by the I/O functions in the Prelude are deﬁned in Chapter 42.

Chapter 8

Foreign Function Interface
The Foreign Function Interface (FFI) has two purposes: it enables (1) to describe in Haskell the interface to foreign language functionality and (2) to use from foreign code Haskell routines. More generally, its aim is to support the implementation of programs in a mixture of Haskell and other languages such that the source code is portable across different implementations of Haskell and non-Haskell systems as well as independent of the architecture and operating system.

8.1

Foreign Languages

The Haskell FFI currently only speciﬁes the interaction between Haskell code and foreign code that follows the C calling convention. However, the design of the FFI is such that it enables the modular extension of the present deﬁnition to include the calling conventions of other programming languages, such as C++ and Java. A precise deﬁnition of the support for those languages is expected to be included in later versions of the language. The second major omission is the deﬁnition of the interaction with multithreading in the foreign language and, in particular, the treatment of thread-local state, and so these details are currently implementation-deﬁned. The core of the present speciﬁcation is independent of the foreign language that is used in conjunction with Haskell. However, there are two areas where FFI speciﬁcations must become language speciﬁc: (1) the speciﬁcation of external names and (2) the marshalling of the basic types of a foreign language. As an example of the former, consider that in C [9] a simple identiﬁer is sufﬁcient to identify an object, while Java [5], in general, requires a qualiﬁed name in conjunction with argument and result types to resolve possible overloading. Regarding the second point, consider that many languages do not specify the exact representation of some basic types. For example the type int in C may be 16, 32, or 64 bits wide. Similarly, Haskell guarantees only that Int covers at least the range [−229 , 229 − 1] (Section 6.4). As a consequence, to reliably represent values of C’s int in Haskell, we have to introduce a new type CInt, which is guaranteed to match the representation of int. The speciﬁcation of external names, dependent on a calling convention, is described in Section 8.5, whereas the marshalling of the basic types in dependence on a foreign language is described in Section 8.6.

91

92

CHAPTER 8. FOREIGN FUNCTION INTERFACE

8.2

Contexts

For a given Haskell system, we deﬁne the Haskell context to be the execution context of the abstract machine on which the Haskell system is based. This includes the heap, stacks, and the registers of the abstract machine and their mapping onto a concrete architecture. We call any other execution context an external context. Generally, we cannot assume any compatibility between the data formats and calling conventions between the Haskell context and a given external context, except where Haskell explicitly prescribes a speciﬁc data format. The principal goal of a foreign function interface is to provide a programmable interface between the Haskell context and external contexts. As a result Haskell threads can access data in external contexts and invoke functions that are executed in an external context as well as vice versa. In the rest of this deﬁnition, external contexts are usually identiﬁed by a calling convention.

8.2.1

Cross Language Type Consistency

Given that many external languages support static types, the question arises whether the consistency of Haskell types with the types of the external language can be enforced for foreign functions. Unfortunately, this is, in general, not possible without a signiﬁcant investment on the part of the implementor of the Haskell system (i.e., without implementing a dedicated type checker). For example, in the case of the C calling convention, the only other approach would be to generate a C prototype from the Haskell type and leave it to the C compiler to match this prototype with the prototype that is speciﬁed in a C header ﬁle for the imported function. However, the Haskell type is lacking some information that would be required to pursue this route. In particular, the Haskell type does not contain any information as to when const modiﬁers have to be emitted. As a consequence, this deﬁnition does not require the Haskell system to check consistency with foreign types. Nevertheless, Haskell systems are encouraged to provide any cross language consistency checks that can be implemented with reasonable effort.

8.3

Lexical Structure

The FFI reserves a single keyword foreign, and a set of special identiﬁers. The latter have a special meaning only within foreign declarations, but may be used as ordinary identiﬁers elsewhere. The special identiﬁers ccall, cplusplus, dotnet, jvm, and stdcall are deﬁned to denote calling conventions. However, a concrete implementation of the FFI is free to support additional, system-speciﬁc calling conventions whose name is not explicitly listed here. To refer to objects of an external C context, we introduce the following phrases: chname cid chchar letter → → → → {chchar } . h letter {letter | ascDigit} letter | ascSymbol & ascSmall | ascLarge | _ (C header ﬁlename) (C identiﬁer)

The range of lexemes that are admissible for chname is a subset of those permitted as arguments to the #include directive in C. In particular, a ﬁle name chname must end in the sufﬁx .h. The lexemes produced by cid coincide with those allowed as C identiﬁers, as speciﬁed in [9].

There are two ﬂavours of foreign declarations: import and export declarations. An import declaration makes an external entity, i.e., a function or memory location deﬁned in an external context, available in the Haskell context. Conversely, an export declaration deﬁnes a function of the Haskell context as an external entity in an external context. Consequently, the two types of declarations differ in that an import declaration deﬁnes a new variable, whereas an export declaration uses a variable that is already deﬁned in the Haskell module. The external context that contains the external entity is determined by the calling convention given in the foreign declaration. Consequently, the exact form of the speciﬁcation of the external entity is dependent on both the calling convention and on whether it appears in an import declaration (as impent) or in an export declaration (as expent). To provide syntactic uniformity in the presence of different calling conventions, it is guaranteed that the description of an external entity lexically appears as a Haskell string lexeme. The only exception is where this string would be the empty string (i.e., be of the form ""); in this case, the string may be omitted in its entirety.

8.4.1

Calling Conventions

The binary interface to an external entity on a given architecture is determined by a calling convention. It often depends on the programming language in which the external entity is implemented, but usually is more dependent on the system for which the external entity has been compiled. As an example of how the calling convention is dominated by the system rather than the programming language, consider that an entity compiled to byte code for the Java Virtual Machine (JVM) [11] needs to be invoked by the rules of the JVM rather than that of the source language in which it is implemented (the entity might be implemented in Oberon, for example). Any implementation of the Haskell FFI must at least implement the C calling convention denoted by ccall. All other calling conventions are optional. Generally, the set of calling conventions is open, i.e., individual implementations may elect to support additional calling conventions. In addition to ccall, Table 8.1 speciﬁes a range of identiﬁers for common calling conventions. Implementations need not implement all of these conventions, but if any is implemented, it must use the listed name. For any other calling convention, implementations are free to choose a suitable name. Only the semantics of the calling conventions ccall and stdcall are deﬁned herein; more calling conventions may be added in future versions of Haskell.

It should be noted that the code generated by a Haskell system to implement a particular calling convention may vary widely with the target code of that system. For example, the calling convention jvm will be trivial to implement for a Haskell compiler generating Java code, whereas for a Haskell compiler generating C code, the Java Native Interface (JNI) [10] has to be targeted.

8.4.2

Foreign Types

The following types constitute the set of basic foreign types: • Char, Int, Double, Float, and Bool as exported by the Haskell Prelude as well as • Int8, Int16, Int32, Int64, Word8, Word16, Word32, Word64, Ptr a, FunPtr a, and StablePtr a, for any type a, as exported by Foreign (Section 24). A Haskell system that implements the FFI needs to be able to pass these types between the Haskell and the external context as function arguments and results. Foreign types are produced according to the following grammar: ftype frtype fatype → | → | → frtype fatype → ftype fatype () qtycon atype1 . . . atypek

(k ≥ 0 )

A foreign type is the Haskell type of an external entity. Only a subset of Haskell’s types are permissible as foreign types, as only a restricted set of types can be canonically transferred between the Haskell context and an external context. A foreign type generally has the form at1 -> · · · -> atn -> rt where n ≥ 0. It implies that the arity of the external entity is n. The argument types ati produced by fatype must be marshallable foreign types; that is, each ati is either (1) a basic foreign type or (2) a type synonym or renamed datatype of a marshallable foreign type. Moreover, the result type rt produced by frtype must be a marshallable foreign result type; that is, it is either a marshallable foreign type, the type (), or a type matching Prelude.IO t, where t is a marshallable foreign type or (). External functions are generally strict in all arguments.

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8.4.3

Import Declarations

Generally, an import declaration has the form foreign import c e v :: t which declares the variable v of type t to be deﬁned externally. Moreover, it speciﬁes that v is evaluated by executing the external entity identiﬁed by the string e using calling convention c. The precise form of e depends on the calling convention and is detailed in Section 8.5. If a variable v is deﬁned by an import declaration, no other top-level declaration for v is allowed in the same module. For example, the declaration
foreign import ccall "string.h strlen" cstrlen :: Ptr CChar -> IO CSize

Such a declaration asserts that the external entity is a true function; i.e., when applied to the same argument values, it always produces the same result. Whether a particular form of external entity places a constraint on the Haskell type with which it can be imported is deﬁned in Section 8.5. Although, some forms of external entities restrict the set of Haskell types that are permissible, the system can generally not guarantee the consistency between the Haskell type given in an import declaration and the argument and result types of the external entity. It is the responsibility of the programmer to ensure this consistency. Optionally, an import declaration can specify, after the calling convention, the safety level that should be used when invoking an external entity. A safe call is less efﬁcient, but guarantees to leave the Haskell system in a state that allows callbacks from the external code. In contrast, an unsafe call, while carrying less overhead, must not trigger a callback into the Haskell system. If it does, the system behaviour is undeﬁned. The default for an invocation is to be safe. Note that a callback into the Haskell system implies that a garbage collection might be triggered after an external entity was called, but before this call returns. Consequently, objects other than stable pointers (cf. Section 36) may be moved or garbage collected by the storage manager.

8.4.4

Export Declarations

The general form of export declarations is foreign export c e v :: t Such a declaration enables external access to v, which may be a value, ﬁeld name, or class method that is declared on the top-level of the same module or imported. Moreover, the Haskell system deﬁnes the external entity described by the string e, which may be used by external code using the calling convention c; an external invocation of the external entity e is translated into evaluation of v. The type t must be an instance of the type of v. For example, we may have
foreign export ccall "addInt" (+) :: Int -> Int -> Int foreign export ccall "addFloat" (+) :: Float -> Float -> Float

If an evaluation triggered by an external invocation of an exported Haskell value returns with an exception, the system behaviour is undeﬁned. Thus, Haskell exceptions have to be caught within Haskell and explicitly marshalled to the foreign code.

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8.5

Speciﬁcation of External Entities

Each foreign declaration has to specify the external entity that is accessed or provided by that declaration. The syntax and semantics of the notation that is required to uniquely determine an external entity depends heavily on the calling convention by which this entity is accessed. For example, for the calling convention ccall, a global label is sufﬁcient. However, to uniquely identify a method in the calling convention jvm, type information has to be provided. For the latter, there is a choice between the Java source-level syntax of types and the syntax expected by JNI—but, clearly, the syntax of the speciﬁcation of an external entity depends on the calling convention and may be non-trivial. Consequently, the FFI does not ﬁx a general syntax for denoting external entities, but requires both impent and expent to take the form of a Haskell string literal. The formation rules for the values of these strings depend on the calling convention and a Haskell system implementing a particular calling convention will have to parse these strings in accordance with the calling convention. Deﬁning impent and expent to take the form of a string implies that all information that is needed to statically analyse the Haskell program is separated from the information needed to generate the code interacting with the foreign language. This is, in particular, helpful for tools processing Haskell source code. When ignoring the entity information provided by impent or expent, foreign import and export declarations are still sufﬁcient to infer identiﬁer deﬁnition and use information as well as type information. For more complex calling conventions, there is a choice between the user-level syntax for identifying entities (e.g., Java or C++) and the system-level syntax (e.g., the type syntax of JNI or mangled C++, respectively). If such a choice exists, the user-level syntax is preferred. Not only because it is more user friendly, but also because the system-level syntax may not be entirely independent of the particular implementation of the foreign language. The following deﬁnes the syntax for specifying external entities and their semantics for the calling conventions ccall and stdcall. Other calling conventions from Table 8.1 are expected to be deﬁned in future versions of Haskell.

8.5.1

Standard C Calls

The following deﬁnes the structure of external entities for foreign declarations under the ccall calling convention for both import and export declarations separately. Afterwards additional constraints on the type of foreign functions are deﬁned. The FFI covers only access to C functions and global variables. There are no mechanisms to access other entities of C programs. In particular, there is no support for accessing pre-processor symbols from Haskell, which includes #defined constants. Access from Haskell to such entities is the domain of language-speciﬁc tools, which provide added convenience over the plain FFI as deﬁned here.

The ﬁrst alternative either imports a static function cid or, if & precedes the identiﬁer, a static address. If cid is omitted, it defaults to the name of the imported Haskell variable. The optional ﬁlename chname speciﬁes a C header ﬁle, where the intended meaning is that the header ﬁle declares the C entity identiﬁed by cid . In particular, when the Haskell system compiles Haskell to C code, the directive #include "chname" needs to be placed into any generated C ﬁle that refers to the foreign entity before the ﬁrst occurrence of that entity in the generated C ﬁle. The second and third alternative, identiﬁed by the keywords dynamic and wrapper, respectively, import stub functions that have to be generated by the Haskell system. In the case of dynamic, the stub converts C function pointers into Haskell functions; and conversely, in the case of wrapper, the stub converts Haskell thunks to C function pointers. If neither of the speciﬁers static, dynamic, or wrapper is given, static is assumed. The speciﬁer static is nevertheless needed to import C routines that are named dynamic or wrapper. It should be noted that a static foreign declaration that does not import an address (i.e., where & is not used in the speciﬁcation of the external entity) always refers to a C function, even if the Haskell type is non-functional. For example,
foreign import ccall foo :: CInt

refers to a pure C function foo with no arguments that returns an integer value. Similarly, if the type is IO CInt, the declaration refers to an impure nullary function. If a Haskell program needs to access a C variable bar of integer type,
foreign import ccall "&" bar :: Ptr CInt

must be used to obtain a pointer referring to the variable. The variable can be read and updated using the routines provided by the module Foreign.Storable (cf. Section 37).

The optional C identiﬁer cid deﬁnes the external name by which the exported Haskell variable is accessible in C. If it is omitted, the external name defaults to the name of the exported Haskell variable.

Constraints on Foreign Function Types In the case of import declaration, there are, depending on the kind of import declaration, constraints regarding the admissible Haskell type that the variable deﬁned in the import may have. These constraints are speciﬁed in the following. Static Functions. A static function can be of any foreign type; in particular, the result type may or may not be in the IO monad. If a function that is not pure is not imported in the IO monad, the system behaviour is undeﬁned. Generally, no check for consistency with the C type of the imported label is performed. As an example, consider

This declaration imports the system() function whose prototype is available from stdlib.h. Static addresses. The type of an imported address is constrained to be of the form Ptr a or FunPtr a, where a can be any type. As an example, consider
foreign import ccall "errno.h &errno" errno :: Ptr CInt

It imports the address of the variable errno, which is of the C type int. Dynamic import. The type of a dynamic stub has to be of the form (FunPtr ft) -> ft, where ft may be any foreign type. As an example, consider
foreign import ccall "dynamic" mkFun :: FunPtr (CInt -> IO ()) -> (CInt -> IO ())

The stub factory mkFun converts any pointer to a C function that gets an integer value as its only argument and does not have a return value into a corresponding Haskell function. Dynamic wrapper. The type of a wrapper stub has to be of the form ft -> IO (FunPtr ft), where ft may be any foreign type. As an example, consider
foreign import ccall "wrapper" mkCallback :: IO () -> IO (FunPtr (IO ()))

The stub factory mkCallback turns any Haskell computation of type IO () into a C function pointer that can be passed to C routines, which can call back into the Haskell context by invoking the referenced function.

Speciﬁcation of Header Files A C header speciﬁed in an import declaration is always included by #include "chname". There is no explicit support for #include <chname> style inclusion. The ISO C99 [7] standard guarantees that any search path that would be used for a #include <chname> is also used for #include "chname" and it is guaranteed that these paths are searched after all paths that are unique to #include "chname". Furthermore, we require that chname ends on .h to make parsing of the speciﬁcation of external entities unambiguous. The speciﬁcation of include ﬁles has been kept to a minimum on purpose. Libraries often require a multitude of include directives, some of which may be system-dependent. Any design that attempts to cover all possible conﬁgurations would introduce signiﬁcant complexity. Moreover, in the current design, a custom include ﬁle can be speciﬁed that uses the standard C preprocessor features to include all relevant headers. Header ﬁles have no impact on the semantics of a foreign call, and whether an implementation uses the header ﬁle or not is implementation-deﬁned. However, as some implementations may require a header ﬁle that supplies a correct prototype for external functions in order to generate correct code, portable FFI code must include suitable header ﬁles.

8.5. SPECIFICATION OF EXTERNAL ENTITIES

99

C Argument Promotion The argument passing conventions of C are dependant on whether a function prototype for the called functions is in scope at a call site. In particular, if no function prototype is in scope, default argument promotion is applied to integral and ﬂoating types. In general, it cannot be expected from a Haskell system that it is aware of whether a given C function was compiled with or without a function prototype being in scope. For the sake of portability, we thus require that a Haskell system generally implements calls to C functions as well as C stubs for Haskell functions as if a function prototype for the called function is in scope. This convention implies that the onus for ensuring the match between C and Haskell code is placed on the FFI user. In particular, when a C function that was compiled without a prototype is called from Haskell, the Haskell signature at the corresponding foreign import declaration must use the types after argument promotion. For example, consider the following C function deﬁnition, which lacks a prototype:
void foo (a) float a; { ... }

The lack of a prototype implies that a C compiler will apply default argument promotion to the parameter a, and thus, foo will expect to receive a value of type double, not float. Hence, the correct foreign import declaration is
foreign import ccall foo :: Double -> IO ()

In contrast, a C function compiled with the prototype
void foo (float a);

requires
foreign import ccall foo :: Float -> IO ()

A similar situation arises in the case of foreign export declarations that use types that would be altered under the C default argument promotion rules. When calling such Haskell functions from C, a function prototype matching the signature provided in the foreign export declaration must be in scope; otherwise, the C compiler will erroneously apply the promotion rules to all function arguments. Note that for a C function deﬁned to a accept a variable number of arguments, all arguments beyond the explicitly typed arguments suffer argument promotion. However, because C permits the calling convention to be different for such functions; a Haskell system will, in general, not be able to make use of variable argument functions. Hence, their use is deprecated in portable code.

8.5.2

Win32 API Calls

The speciﬁcation of external entities under the stdcall calling convention is identical to that for standard C calls. The two calling conventions only differ in the generated code.

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8.6

Marshalling

In addition to the language extension discussed in previous sections, the FFI includes a set of standard libraries, which ease portable use of foreign functions as well as marshalling of compound structures. Generally, the marshalling of Haskell structures into a foreign representation and vice versa can be implemented in either Haskell or the foreign language. At least where the foreign language is at a signiﬁcantly lower level, e.g. C, there are good reasons for doing the marshalling in Haskell: • Haskell’s lazy evaluation strategy would require any foreign code that attempts to access Haskell structures to force the evaluation of these structures before accessing them. This would lead to complicated code in the foreign language, but does not need any extra consideration when coding the marshalling in Haskell. • Despite the fact that marshalling code in Haskell tends to look like C in Haskell syntax, the strong type system still catches many errors that would otherwise lead to difﬁcult-to-debug runtime faults. • Direct access to Haskell heap structures from a language like C—especially, when marshalling from C to Haskell, i.e., when Haskell structures are created—carries the risk of corrupting the heap, which usually leads to faults that are very hard to debug. Consequently, the Haskell FFI emphasises Haskell-side marshalling. The interface to the marshalling libraries is provided by the module Foreign (Chapter 24) plus a languagedependent module per supported language. In particular, the standard requires the availability of the module Foreign.C (Chapter 25), which simpliﬁes portable interfacing with external C code. Language-dependent modules, such as Foreign.C, generally provide Haskell types representing the basic types of the foreign language using a representation that is compatible with the foreign types as implemented by the default implementation of the foreign language on the present architecture. This is especially important for languages where the standard leaves some aspects of the implementation of basic types open. For example, in C, the size of the various integral types is not ﬁxed. Thus, to represent C interfaces faithfully in Haskell, for each integral type in C, we need to have an integral type in Haskell that is guaranteed to have the same size as the corresponding C type.

8.7

The External C Interface

Every Haskell system that implements the FFI needs to provide a C header ﬁle named HsFFI.h that deﬁnes the C symbols listed in Tables 8.2 and 8.3. Table 8.2 table lists symbols that represent types together with the Haskell type that they represent and any constraints that are placed on the concrete C types that implement these symbols. When a C type HsT represents a Haskell type T, the occurrence of T in a foreign function declaration should be matched by HsT in the corresponding C function prototype. Indeed, where the Haskell system translates Haskell to C code that invokes foreign imported C routines, such prototypes need to be provided and included via the header that can be speciﬁed in external entity strings for foreign C functions (cf. Section 8.5.1); otherwise, the system behaviour is undeﬁned. It is guaranteed that the Haskell value nullPtr is mapped to (HsPtr) NULL in C and nullFunPtr is mapped to (HsFunPtr) NULL and vice versa. Table 8.3 contains symbols characterising the range and precision of the types from Table 8.2. Where available, the table states the corresponding Haskell values. All C symbols, with the exception of

HS_FLOAT_ROUND are constants that are suitable for use in #if preprocessing directives. Note that there is only one rounding style (HS_FLOAT_ROUND) and one radix (HS_FLOAT_RADIX), as this is all that is supported by ISO C [7]. Moreover, an implementation that does not support 64 bit integral types on the C side should implement HsInt64 and HsWord64 as a structure. In this case, the bounds HS_INT64_MIN, HS_INT64_MAX, and HS_WORD64_MAX are undeﬁned. In addition, to the symbols from Table 8.2 and 8.3, the header HsFFI.h must also contain the following prototypes: void hs_init (int *argc, char **argv[]); void hs_exit (void); void hs_set_argv (int argc, char *argv[]); void hs_perform_gc (void); void hs_free_stable_ptr (HsStablePtr sp); void hs_free_fun_ptr (HsFunPtr fp); These routines are useful for mixed language programs, where the main application is implemented in a foreign language that accesses routines implemented in Haskell. The function hs_init() initialises the Haskell system and provides it with the available command line arguments. Upon return, the arguments solely intended for the Haskell runtime system are removed (i.e., the values that argc and argv point to may have changed). This function must be called during program startup before any Haskell function is invoked; otherwise, the system behaviour is undeﬁned. Conversely, the Haskell system is deinitialised by a call to hs_exit(). Multiple invocations of hs_init() are permitted, provided that they are followed by an equal number of calls to hs_exit() and that the ﬁrst call to hs_exit() is after the last call to hs_init(). In addition to nested calls to hs_init(), the Haskell system may be de-initialised with

rounding style as per [7] difference between 1 and the least value greater than 1 as per [7] (as above) number of decimal digits as per [7] (as above)

minimum ﬂoating point number as per [7] (as above)

minimum decimal exponent as per [7] (as above) maximum ﬂoating point number as per [7] (as above)

maximum decimal exponent as per [7] (as above)

Table 8.3: C Interface to Range and Precision of Basic Types

8.7. THE EXTERNAL C INTERFACE

103

hs_exit() and be re-initialised with hs_init() at a later point in time. This ensures that repeated initialisation due to multiple libraries being implemented in Haskell is covered. The Haskell system will ignore the command line arguments passed to the second and any following calls to hs_init(). Moreover, hs_init() may be called with NULL for both argc and argv, signalling the absence of command line arguments. The function hs_set_argv() sets the values returned by the functions getProgName and getArgs of the module System.Environment (Section 39). This function may only be invoked after hs_init(). Moreover, if hs_set_argv() is called at all, this call must precede the ﬁrst invocation of getProgName and getArgs. Note that the separation of hs_init() and hs_set_argv() is essential in cases where in addition to the Haskell system other libraries that process command line arguments during initialisation are used. The function hs_perform_gc() advises the Haskell storage manager to perform a garbage collection, where the storage manager makes an effort to releases all unreachable objects. This function must not be invoked from C functions that are imported unsafe into Haskell code nor may it be used from a ﬁnalizer. Finally, hs_free_stable_ptr() and hs_free_fun_ptr() are the C counterparts of the Haskell functions freeStablePtr and freeHaskellFunPtr.

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Chapter 9

Standard Prelude
In this chapter the entire Haskell Prelude is given. It constitutes a speciﬁcation for the Prelude. Many of the deﬁnitions are written with clarity rather than efﬁciency in mind, and it is not required that the speciﬁcation be implemented as shown here. The default method deﬁnitions, given with class declarations, constitute a speciﬁcation only of the default method. They do not constitute a speciﬁcation of the meaning of the method in all instances. To take one particular example, the default method for enumFrom in class Enum will not work properly for types whose range exceeds that of Int (because fromEnum cannot map all values in the type to distinct Int values). The Prelude shown here is organized into a root module, Prelude, and three sub-modules, PreludeList, PreludeText, and PreludeIO. This structure is purely presentational. An implementation is not required to use this organisation for the Prelude, nor are these three modules available for import separately. Only the exports of module Prelude are signiﬁcant. Some of these modules import Library modules, such as Data.Char, Control.Monad, System.IO, and Numeric. These modules are described fully in Part II. These imports are not, of course, part of the speciﬁcation of the Prelude. That is, an implementation is free to import more, or less, of the Library modules, as it pleases. Primitives that are not deﬁnable in Haskell, indicated by names starting with “prim”, are deﬁned in a system dependent manner in module PreludeBuiltin and are not shown here. Instance declarations that simply bind primitives to class methods are omitted. Some of the more verbose instances with obvious functionality have been left out for the sake of brevity. Declarations for special types such as Integer, or () are included in the Prelude for completeness even though the declaration may be incomplete or syntactically invalid. An ellipsis “...” is often used in places where the remainder of a deﬁnition cannot be given in Haskell. To reduce the occurrence of unexpected ambiguity errors, and to improve efﬁciency, a number of commonlyused functions over lists use the Int type rather than using a more general numeric type, such as Integral a or Num a. These functions are: take, drop, !!, length, splitAt, and replicate. The more general versions are given in the Data.List library, with the preﬁx “generic”; for example genericLength.

The Enum instances for Floats and Doubles are slightly unusual. The ‘toEnum’ function truncates numbers to Int. The definitions of enumFrom and enumFromThen allow floats to be used in arithmetic series: [0,0.1 .. 0.95]. However, roundoff errors make these somewhat dubious. This example may have either 10 or 11 elements, depending on how 0.1 is represented. where x+1 x-1 fromIntegral fromInteger . truncate numericEnumFrom numericEnumFromThen numericEnumFromTo numericEnumFromThenTo

-- It is expected that compilers will recognize this and insert error -- messages that are more appropriate to the context in which undefined -- appears. undefined undefined :: a = error "Prelude.undefined"

The zipWith family generalises the zip family by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

In both the lexical and the context-free syntax, there are some ambiguities that are to be resolved by making grammatical phrases as long as possible, proceeding from left to right (in shift-reduce parsing, resolving shift/reduce conﬂicts by shifting). In the lexical syntax, this is the “maximal munch” rule. In the context-free syntax, this means that conditionals, let-expressions, and lambda abstractions extend to the right as far as possible.

Section 2.7 gives an informal discussion of the layout rule. This section deﬁnes it more precisely. The meaning of a Haskell program may depend on its layout. The effect of layout on its meaning can be completely described by adding braces and semicolons in places determined by the layout. The meaning of this augmented program is now layout insensitive.

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The effect of layout is speciﬁed in this section by describing how to add braces and semicolons to a laid-out program. The speciﬁcation takes the form of a function L that performs the translation. The input to L is: • A stream of lexemes as speciﬁed by the lexical syntax in the Haskell report, with the following additional tokens: – If a let, where, do, or of keyword is not followed by the lexeme {, the token {n} is inserted after the keyword, where n is the indentation of the next lexeme if there is one, or 0 if the end of ﬁle has been reached. – If the ﬁrst lexeme of a module is not { or module, then it is preceded by {n} where n is the indentation of the lexeme. – Where the start of a lexeme is preceded only by white space on the same line, this lexeme is preceded by < n > where n is the indentation of the lexeme, provided that it is not, as a consequence of the ﬁrst two rules, preceded by {n}. (NB: a string literal may span multiple lines – Section 2.6. So in the fragment
f = ("Hello \ \Bill", "Jake")

There is no < n > inserted before the \Bill, because it is not the beginning of a complete lexeme; nor before the ,, because it is not preceded only by white space.) • A stack of “layout contexts”, in which each element is either: – Zero, indicating that the enclosing context is explicit (i.e. the programmer supplied the opening brace. If the innermost context is 0, then no layout tokens will be inserted until either the enclosing context ends or a new context is pushed. – A positive integer, which is the indentation column of the enclosing layout context. The “indentation” of a lexeme is the column number of the ﬁrst character of that lexeme; the indentation of a line is the indentation of its leftmost lexeme. To determine the column number, assume a ﬁxed-width font with the following conventions: • The characters newline, return, linefeed , and formfeed , all start a new line. • The ﬁrst column is designated column 1, not 0. • Tab stops are 8 characters apart. • A tab character causes the insertion of enough spaces to align the current position with the next tab stop. For the purposes of the layout rule, Unicode characters in a source program are considered to be of the same, ﬁxed, width as an ASCII character. However, to avoid visual confusion, programmers should avoid writing programs in which the meaning of implicit layout depends on the width of non-space characters. The application L tokens [] delivers a layout-insensitive translation of tokens, where tokens is the result of lexically analysing a module and adding column-number indicators to it as described above. The deﬁnition of L is as follows, where we use “:” as a stream construction operator, and “[ ]” for the empty stream.

Here, the deﬁnition of p is indented less than the indentation of the enclosing context, which is set in this case by the deﬁnition of h. Note 2. If the ﬁrst token after a where (say) is not indented more than the enclosing layout context, then the block must be empty, so empty braces are inserted. The {n} token is replaced by < n >, to mimic the situation if the empty braces had been explicit. Note 3. By matching against 0 for the current layout context, we ensure that an explicit close brace can only match an explicit open brace. A parse error results if an explicit close brace matches an implicit open brace. Note 4. This clause means that all brace pairs are treated as explicit layout contexts, including labelled construction and update (Section 3.15). This is a difference between this formulation and Haskell 1.4. Note 5. The side condition parse-error(t) is to be interpreted as follows: if the tokens generated so far by L together with the next token t represent an invalid preﬁx of the Haskell grammar, and the tokens generated so far by L followed by the token “}” represent a valid preﬁx of the Haskell grammar, then parse-error(t) is true. The test m/ = 0 checks that an implicitly-added closing brace would match an implicit open brace. Note 6. At the end of the input, any pending close-braces are inserted. It is an error at this point to be within a non-layout context (i.e. m = 0 ).

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If none of the rules given above matches, then the algorithm fails. It can fail for instance when the end of the input is reached, and a non-layout context is active, since the close brace is missing. Some error conditions are not detected by the algorithm, although they could be: for example let }. Note 1 implements the feature that layout processing can be stopped prematurely by a parse error. For example
let x = e; y = x in e’

is valid, because it translates to
let { x = e; y = x } in e’

The close brace is inserted due to the parse error rule above.

10.4. LITERATE COMMENTS

135

10.4

Literate comments

The “literate comment” convention, ﬁrst developed by Richard Bird and Philip Wadler for Orwell, and inspired in turn by Donald Knuth’s “literate programming”, is an alternative style for encoding Haskell source code. The literate style encourages comments by making them the default. A line in which “>” is the ﬁrst character is treated as part of the program; all other lines are comment. The program text is recovered by taking only those lines beginning with “>”, and replacing the leading “>” with a space. Layout and comments apply exactly as described in Chapter 10 in the resulting text. To capture some cases where one omits an “>” by mistake, it is an error for a program line to appear adjacent to a non-blank comment line, where a line is taken as blank if it consists only of whitespace. By convention, the style of comment is indicated by the ﬁle extension, with “.hs” indicating a usual Haskell ﬁle and “.lhs” indicating a literate Haskell ﬁle. Using this style, a simple factorial program would be:
This literate program prompts the user for a number and prints the factorial of that number: > main :: IO () > main = do putStr "Enter a number: " > l <- readLine > putStr "n!= " > print (fact (read l)) This is the factorial function. > fact :: Integer -> Integer > fact 0 = 1 > fact n = n * fact (n-1)

An alternative style of literate programming is particularly suitable for use with the LaTeX text processing system. In this convention, only those parts of the literate program that are entirely enclosed between \begin{code}. . .\end{code} delimiters are treated as program text; all other lines are comment. More precisely: • Program code begins on the ﬁrst line following a line that begins \begin{code}. • Program code ends just before a subsequent line that begins \end{code} (ignoring string literals, of course). It is not necessary to insert additional blank lines before or after these delimiters, though it may be stylistically desirable. For example,
\documentstyle{article} \begin{document} \chapter{Introduction} This is a trivial program that prints the first 20 factorials.

The following is an example implementation of ﬁxity resolution for Haskell expressions. Fixity resolution also applies to Haskell patterns, but patterns are a subset of expressions so in what follows we consider only expressions for simplicity. The function resolve takes a list in which the elements are expressions or operators, i.e. an instance of the inﬁxexp non-terminal in the context-free grammar. It returns either Just e where e is the resolved expression, or Nothing if the input does not represent a valid expression. In a compiler, of course, it would be better to return more information about the operators involved for the purposes of producing a useful error message, but the Maybe type will sufﬁce to illustrate the algorithm here.
import Control.Monad type Prec type Var = Int = String

The algorithm works as follows. At each stage we have a call
parse op1 E1 (op2 : tokens)

which means that we are looking at an expression like
E0 ‘op1‘ E1 ‘op2‘ ... (1)

(the caller holds E0). The job of parse is to build the expression to the right of op1, returning the expression and any remaining input. There are three cases to consider: 1. if op1 and op2 have the same precedence, but they do not have the same associativity, or they are declared to be nonﬁx, then the expression is illegal. 2. If op1 has a higher precedence than op2, or op1 and op2 should left-associate, then we know that the expression to the right of op1 is E1, so we return this to the caller. 3. Otherwise, we know we want to build an expression of the form E1 ‘op2‘ R. To ﬁnd R, we call parseNeg op2 tokens to compute the expression to the right of op2, namely R (more about parseNeg below, but essentially if tokens is of the form (E2 : rest), then this is equivalent to parse op2 E2 rest). Now, we have E0 ‘op1‘ (E1 ‘op2‘ R) ‘op3‘ ... where op3 is the next operator in the input. This is an instance of (1) above, so to continue we call parse, with the new E1 == (E1 ‘op2‘ R). To initialise the algorithm, we set op1 to be an imaginary operator with precedence lower than anyything else. Hence parse will consume the whole input, and return the resulting expression. The handling of the preﬁx negation operator, -, complicates matters only slightly. Recall that preﬁx negation has the same ﬁxity as inﬁx negation: left-associative with precedence 6. The operator to the left of -, if there is one, must have precedence lower than 6 for the expression to be legal. The negation operator itself may left-associate with operators of the same ﬁxity (e.g. +). So for example -a + b is legal and resolves as (-a) + b, but a + -b is illegal. The function parseNeg handles preﬁx negation. If we encounter a negation operator, and it is legal in this position (the operator to the left has precedence lower than 6), then we proceed in a similar way to case (3) above: compute the argument to - by recursively calling parseNeg, and then continue by calling parse. Note that this algorithm is insensitive to the range and resolution of precedences. There is no reason in principle that Haskell should be limited to integral precedences in the range 1 to 10; a larger range, or fractional values, would present no additional difﬁculties.

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CHAPTER 10. SYNTAX REFERENCE

Chapter 11

Speciﬁcation of Derived Instances
A derived instance is an instance declaration that is generated automatically in conjunction with a data or newtype declaration. The body of a derived instance declaration is derived syntactically from the deﬁnition of the associated type. Derived instances are possible only for classes known to the compiler: those deﬁned in either the Prelude or a standard library. In this chapter, we describe the derivation of classes deﬁned by the Prelude. If T is an algebraic datatype declared by: data cx => T u1 . . . uk = K1 t11 . . . t1k1 | · · · | Kn tn1 . . . tnkn deriving (C1 , . . . , Cm )

(where m ≥ 0 and the parentheses may be omitted if m = 1 ) then a derived instance declaration is possible for a class C if these conditions hold: 1. C is one of Eq, Ord, Enum, Bounded, Show, or Read. 2. There is a context cx such that cx ⇒ C tij holds for each of the constituent types tij . 3. If C is Bounded, the type must be either an enumeration (all constructors must be nullary) or have only one constructor. 4. If C is Enum, the type must be an enumeration. 5. There must be no explicit instance declaration elsewhere in the program that makes T u1 . . . uk an instance of C . 6. If the data declaration has no constructors (i.e. when n = 0 ), then no classes are derivable (i.e. m = 0 ) For the purposes of derived instances, a newtype declaration is treated as a data declaration with a single constructor. If the deriving form is present, an instance declaration is automatically generated for T u1 . . . uk over each class Ci . If the derived instance declaration is impossible for any of the Ci then a static error results. If no derived instances are required, the deriving form may be omitted or the form deriving () may be used. 145

146

CHAPTER 11. SPECIFICATION OF DERIVED INSTANCES

Each derived instance declaration will have the form: instance (cx , cx ) => Ci (T u1 . . . uk ) where { d } where d is derived automatically depending on Ci and the data type declaration for T (as will be described in the remainder of this section). The context cx is the smallest context satisfying point (2) above. For mutually recusive data types, the compiler may need to perform a ﬁxpoint calculation to compute it. The remaining details of the derived instances for each of the derivable Prelude classes are now given. Free variables and constructors used in these translations always refer to entities deﬁned by the Prelude.

11.1

Derived instances of Eq and Ord

The class methods automatically introduced by derived instances of Eq and Ord are (==), (/=), compare, (<), (<=), (>), (>=), max, and min. The latter seven operators are deﬁned so as to compare their arguments lexicographically with respect to the constructor set given, with earlier constructors in the datatype declaration counting as smaller than later ones. For example, for the Bool datatype, we have that (True > False) == True. Derived comparisons always traverse constructors from left to right. These examples illustrate this property:
(1,undefined) == (2,undefined) @"\Rightarrow"@ (undefined,1) == (undefined,2) @"\Rightarrow"@ False @"\bot"@

All derived operations of class Eq and Ord are strict in both arguments. For example, False <= ⊥ is ⊥, even though False is the ﬁrst constructor of the Bool type.

11.2

Derived instances of Enum

Derived instance declarations for the class Enum are only possible for enumerations (data types with only nullary constructors). The nullary constructors are assumed to be numbered left-to-right with the indices 0 through n − 1. The succ and pred operators give the successor and predecessor respectively of a value, under this numbering scheme. It is an error to apply succ to the maximum element, or pred to the minimum element. The toEnum and fromEnum operators map enumerated values to and from the Int type; toEnum raises a runtime error if the Int argument is not the index of one of the constructors. The deﬁnitions of the remaining methods are
enumFrom x enumFromThen x y = enumFromTo x lastCon = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = | otherwise = enumFromTo x y = map toEnum [fromEnum x .. fromEnum enumFromThenTo x y z = map toEnum [fromEnum x, fromEnum y

lastCon firstCon y] .. fromEnum z]

11.3. DERIVED INSTANCES OF BOUNDED

147

where firstCon and lastCon are respectively the ﬁrst and last constructors listed in the data declaration. For example, given the datatype:
data Color = Red | Orange | Yellow | Green deriving (Enum)

The Bounded class introduces the class methods minBound and maxBound, which deﬁne the minimal and maximal elements of the type. For an enumeration, the ﬁrst and last constructors listed in the data declaration are the bounds. For a type with a single constructor, the constructor is applied to the bounds for the constituent types. For example, the following datatype:
data Pair a b = Pair a b deriving Bounded

The class methods automatically introduced by derived instances of Read and Show are showsPrec, readsPrec, showList, and readList. They are used to coerce values into strings and parse strings into values. The function showsPrec d x r accepts a precedence level d (a number from 0 to 11), a value x, and a string r. It returns a string representing x concatenated to r. showsPrec satisﬁes the law: showsPrec d x r ++ s == showsPrec d x (r ++ s)

The representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d. Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression (recall that function application has precedence 10). The extra parameter r is essential if tree-like structures are to be printed in linear time rather than time quadratic in the size of the tree. The function readsPrec d s accepts a precedence level d (a number from 0 to 10) and a string s, and attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty. Parsing of an un-parenthesised inﬁx operator application succeeds only if the precedence of the operator is greater than or equal to d. It should be the case that

That is, readsPrec should be able to parse the string produced by showsPrec, and should deliver the value that showsPrec started with. showList and readList allow lists of objects to be represented using non-standard denotations. This is especially useful for strings (lists of Char). readsPrec will parse any valid representation of the standard types apart from strings, for which only quoted strings are accepted, and other lists, for which only the bracketed form [. . . ] is accepted. See Chapter 9 for full details. The result of show is a syntactically correct Haskell expression containing only constants, given the ﬁxity declarations in force at the point where the type is declared. It contains only the constructor names deﬁned in the data type, parentheses, and spaces. When labelled constructor ﬁelds are used, braces, commas, ﬁeld names, and equal signs are also used. Parentheses are only added where needed, ignoring associativity. No line breaks are added. The result of show is readable by read if all component types are readable. (This is true for all instances deﬁned in the Prelude but may not be true for user-deﬁned instances.) Derived instances of Read make the following assumptions, which derived instances of Show obey: • If the constructor is deﬁned to be an inﬁx operator, then the derived Read instance will parse only inﬁx applications of the constructor (not the preﬁx form). • Associativity is not used to reduce the occurrence of parentheses, although precedence may be. For example, given
infixr 4 :$ data T = Int :$ T | NT

then: – show (1 :$ 2 :$ NT) produces the string "1 :$ (2 :$ NT)". – read "1 :$ (2 :$ NT)" succeeds, with the obvious result. – read "1 :$ 2 :$ NT" fails. • If the constructor is deﬁned using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the ﬁelds must be given in the same order as the original declaration. • The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed. The derived Read and Show instances may be unsuitable for some uses. Some problems include: • Circular structures cannot be printed or read by these instances. • The printer loses shared substructure; the printed representation of an object may be much larger than necessary. • The parsing techniques used by the reader are very inefﬁcient; reading a large structure may be quite slow. • There is no user control over the printing of types deﬁned in the Prelude. For example, there is no way to change the formatting of ﬂoating point numbers.

Automatic derivation of instance declarations for Bounded and Enum are not possible, as Tree is not an enumeration or single-constructor datatype. The complete instance declarations for Tree are shown in Figure 11.1, Note the implicit use of default class method deﬁnitions—for example, only <= is deﬁned for Ord, with the other class methods (<, >, >=, max, and min) being deﬁned by the defaults given in the class declaration shown in Figure 6.1.

Compiler Pragmas
Some compiler implementations support compiler pragmas, which are used to give additional instructions or hints to the compiler, but which do not form part of the Haskell language proper and do not change a program’s semantics. This chapter summarizes this existing practice. An implementation is not required to respect any pragma, although pragmas that are not recognised by the implementation should be ignored. Implementations are strongly encouraged to support the LANGUAGE pragma described below as there are many language extensions being used in practice. Lexically, pragmas appear as comments, except that the enclosing syntax is {-# #-}.

12.1
decl decl

Inlining
→ → {-# INLINE qvars #-} {-# NOINLINE qvars #-}

The INLINE pragma instructs the compiler to inline the speciﬁed variables at their use sites. Compilers will often automatically inline simple expressions. This may be prevented by the NOINLINE pragma.

calls to factorial in which the compiler can detect that the parameter is either Int or Integer will use specialized versions of factorial which do not involve overloaded numeric operations. 151

152

CHAPTER 12. COMPILER PRAGMAS

12.3

Language extensions

The LANGUAGE pragma is a ﬁle-header pragma. A ﬁle-header pragma must precede the module keyword in a source ﬁle. There can be as many ﬁle-header pragmas as you please, and they can be preceded or followed by comments. An individual language pragma begins with the keyword LANGUAGE and is followed by a comma-separated list of named language features. For example, to enable scoped type variables and preprocessing with CPP, if your Haskell implementation supports these extensions:
{-# LANGUAGE ScopedTypeVariables, CPP #-}

If a Haskell implementation does not recognize or support a particular language feature that a source ﬁle requests (or cannot support the combination of language features requested), any attempt to compile or otherwise use that ﬁle with that Haskell implementation must fail with an error. In the interests of portability, multiple attempts to enable the same, supported language features (e.g. via command-line arguments, implementation-speciﬁc features dependencies or non-standard pragmas) are speciﬁcally permitted. Haskell 2010 implementations that support the LANGUAGE pragma are required to support
{-# LANGUAGE Haskell2010 #-}

Those implementations are also encouraged to support the following named language features:
PatternGuards, NoNPlusKPatterns, RelaxedPolyRec, EmptyDataDecls, ForeignFunctionInterface

These are the named language extensions supported by some pre-Haskell 2010 implementations, that have been integrated into this report.

The Monad class deﬁnes the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell’s do expressions provide a convenient syntax for writing monadic expressions. Minimal complete deﬁnition: >>= and return. Instances of Monad should satisfy the following laws:
return a >>= k == k a m >>= return == m m >>= (\x -> k x >>= h)

Sequentially compose two actions, passing any value produced by the ﬁrst as an argument to the second.
(>>) :: m a -> m b -> m b

Sequentially compose two actions, discarding any value produced by the ﬁrst, like sequencing operators (such as the semicolon) in imperative languages.
return :: a -> m a

Inject a value into the monadic type.
fail :: String -> m a

Fail with a message. This operation is not part of the mathematical deﬁnition of a monad, but is invoked on pattern-match failure in a do expression.
instance Monad [] instance Monad IO instance Monad Maybe

class Monad m => MonadPlus m where

Monads that also support choice and failure. Methods
mzero :: m a

the identity of mplus. It should also satisfy the equations
mzero >>= f v >> mzero = = mzero mzero

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the ‘folded function’ are not commutative.
foldM f a1 [x1, x2, ..., xm]

Haskell provides indexable arrays, which may be thought of as functions whose domains are isomorphic to contiguous subsets of the integers. Functions restricted in this way can be implemented efﬁciently; in particular, a programmer may reasonably expect rapid access to the components. To ensure the possibility of such an implementation, arrays are treated as data, not as general functions. Since most array functions involve the class Ix, the contents of the module Data.Ix are re-exported from Data.Array for convenience:
module Data.Ix

a pair of bounds, each of the index type of the array. These bounds are the lowest and highest indices in the array, in that order. For example, a one-origin vector of length ’10’ has bounds ’(1,10)’, and a one-origin ’10’ by ’10’ matrix has bounds ’((1,1),(10,10))’. a list of associations of the form (index, value). Typically, this list will be expressed as a comprehension. An association ’(i, x)’ deﬁnes the value of the array at index i to be x.

->

Array i e

Construct an array with the speciﬁed bounds and containing values for given indices within these bounds. The array is undeﬁned (i.e. bottom) if any index in the list is out of bounds. If any two associations in the list have the same index, the value at that index is undeﬁned (i.e. bottom). Because the indices must be checked for these errors, array is strict in the bounds argument and in the indices of the association list, but non-strict in the values. Thus, recurrences such as the following are possible:
a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i <- [2..100]])

Not every index within the bounds of the array need appear in the association list, but the values associated with indices that do not appear will be undeﬁned (i.e. bottom). If, in any dimension, the lower bound is greater than the upper bound, then the array is legal, but empty. Indexing an empty array always gives an array-bounds error, but bounds still yields the bounds with which the array was constructed.
listArray :: Ix i => (i, i) -> [e] -> Array i e

The accumArray function deals with repeated indices in the association list using an accumulating function which combines the values of associations with the same index. For example, given a list of values of some index type, hist produces a histogram of the number of occurrences of each index within a speciﬁed range:
hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b hist bnds is = accumArray (+) 0 bnds [(i, 1) | i<-is, inRange bnds i]

If the accumulating function is strict, then accumArray is strict in the values, as well as the indices, in the association list. Thus, unlike ordinary arrays built with array, accumulated arrays should not in general be recursive.

14.3. ACCESSING ARRAYS

163

14.3

Accessing arrays

(!) :: Ix i => Array i e -> i -> e

The value at the given index in an array.
bounds :: Ix i => Array i e -> (i, i)

The bounds with which an array was constructed.
indices :: Ix i => Array i e -> [i]

The list of indices of an array in ascending order.
elems :: Ix i => Array i e -> [e]

The list of elements of an array in index order.
assocs :: Ix i => Array i e -> [(i, e)]

The list of associations of an array in index order.

14.4

Incremental array updates

(//) :: Ix i => Array i e -> [(i, e)] -> Array i e

Constructs an array identical to the ﬁrst argument except that it has been updated by the associations in the right argument. For example, if m is a 1-origin, n by n matrix, then
m//[((i,i), 0) | i <- [1..n]]

is the same matrix, except with the diagonal zeroed. Repeated indices in the association list are handled as for array: the resulting array is undeﬁned (i.e. bottom),
accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e accum f takes an array and an association list and accumulates pairs from the list into the array with the accumulating function f. Thus accumArray can be deﬁned using accum: accumArray f z b = accum f (array b [(i, z) | i <- range b])

Reverse all the bits in the argument
shift :: a -> Int -> a shift x i shifts x left by i bits if i is positive, or right by -i bits otherwise. Right shifts perform sign extension on signed number types; i.e. they ﬁll the top bits with 1 if the x is negative

and with 0 otherwise. An instance can deﬁne either this uniﬁed shift or shiftL and shiftR, depending on which is more convenient for the type in question.
rotate :: a -> Int -> a rotate x i rotates x left by i bits if i is positive, or right by -i bits otherwise.

For unbounded types like Integer, rotate is equivalent to shift. An instance can deﬁne either this uniﬁed rotate or rotateL and rotateR, depending on which is more convenient for the type in question.
bit :: Int -> a bit i is a value with the ith bit set setBit :: a -> Int -> a x ‘setBit‘ i is the same as x .|. bit i clearBit :: a -> Int -> a x ‘clearBit‘ i is the same as x .&. complement (bit i) complementBit :: a -> Int -> a x ‘complementBit‘ i is the same as x ‘xor‘ bit i testBit :: a -> Int -> Bool

Return True if the nth bit of the argument is 1
bitSize :: a -> Int

Return the number of bits in the type of the argument. The actual value of the argument is ignored. The function bitSize is undeﬁned for types that do not have a ﬁxed bitsize, like Integer.
isSigned :: a -> Bool

Return True if the argument is a signed type. The actual value of the argument is ignored

169
shiftL :: a -> Int -> a

Shift the argument left by the speciﬁed number of bits (which must be non-negative). An instance can deﬁne either this and shiftR or the uniﬁed shift, depending on which is more convenient for the type in question.
shiftR :: a -> Int -> a

Shift the ﬁrst argument right by the speciﬁed number of bits (which must be non-negative). Right shifts perform sign extension on signed number types; i.e. they ﬁll the top bits with 1 if the x is negative and with 0 otherwise. An instance can deﬁne either this and shiftL or the uniﬁed shift, depending on which is more convenient for the type in question.
rotateL :: a -> Int -> a

Rotate the argument left by the speciﬁed number of bits (which must be non-negative). An instance can deﬁne either this and rotateR or the uniﬁed rotate, depending on which is more convenient for the type in question.
rotateR :: a -> Int -> a

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) characters (see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the ﬁrst 256 charachers), which is itself an extension of the ASCII character set (the ﬁrst 128 characters). A character literal in Haskell has type Char. To convert a Char to or from the corresponding Int value deﬁned by Unicode, use Prelude.toEnum and Prelude.fromEnum from the Prelude.Enum class respectively (or equivalently ord and chr).
instance instance instance instance instance instance instance instance Bounded Char Enum Char Eq Char Ord Char Read Char Show Char Ix Char Storable Char

type String = [Char]

A String is a list of characters. String constants in Haskell are values of type String.

Selects alphabetic or numeric digit Unicode characters. Note that numeric digits outside the ASCII range are selected by this function but not by isDigit. Such digits may be part of identiﬁers but are not used by the printer and reader to represent numbers.
isPrint :: Char -> Bool

Convert a letter to the corresponding upper-case letter, if any. Any other character is returned unchanged.
toLower :: Char -> Char

Convert a letter to the corresponding lower-case letter, if any. Any other character is returned unchanged.
toTitle :: Char -> Char

Convert a letter to the corresponding title-case or upper-case letter, if any. (Title case differs from upper case only for a small number of ligature letters.) Any other character is returned unchanged.

Extracts the real part of a complex number.
imagPart :: RealFloat a => Complex a -> a

Extracts the imaginary part of a complex number. 177

178

CHAPTER 17. DATA.COMPLEX

17.2

Polar form

mkPolar :: RealFloat a => a -> a -> Complex a

Form a complex number from polar components of magnitude and phase.
cis :: RealFloat a => a -> Complex a cis t is a complex value with magnitude 1 and phase t (modulo 2*pi).

polar :: RealFloat a => Complex a -> (a, a)

The function polar takes a complex number and returns a (magnitude, phase) pair in canonical form: the magnitude is nonnegative, and the phase in the range (-pi, pi]; if the magnitude is zero, then so is the phase.
magnitude :: RealFloat a => Complex a -> a

The nonnegative magnitude of a complex number.
phase :: RealFloat a => Complex a -> a

The phase of a complex number, in the range (-pi, pi]. If the magnitude is zero, then so is the phase.

This module provides signed integer types of unspeciﬁed width (Int) and ﬁxed widths (Int8, Int16, Int32 and Int64). All arithmetic is performed modulo 2ˆn, where n is the number of bits in the type. For coercing between any two integer types, use fromIntegral. Coercing word types (see Data.Word) to and from integer types preserves representation, not sign. The rules that hold for Enum instances over a bounded type such as Int (see the section of the Haskell language report dealing with arithmetic sequences) also hold for the Enum instances over the various Int types deﬁned here. Right and left shifts by amounts greater than or equal to the width of the type result in either zero or -1, depending on the sign of the value being shifted. This is contrary to the behaviour in C, which is undeﬁned; a common interpretation is to truncate the shift count to the width of the type, for example 1 << 32 == 1 in some C implementations.
data Int

A ﬁxed-precision integer type with at least the range [-2ˆ29 .. 2ˆ29-1]. The exact range for a given implementation can be determined by using Prelude.minBound and Prelude.maxBound from the Prelude.Bounded class.

The Ix class is used to map a contiguous subrange of values in a type onto integers. It is used primarily for array indexing (see the array package). The ﬁrst argument (l,u) of each of these operations is a pair specifying the lower and upper bounds of a contiguous subrange of values. An implementation is entitled to assume the following laws about these operations: • inRange (l,u) i == elem i (range (l,u)) • range (l,u) !! index (l,u) i == i, when inRange (l,u) i • map (index (l,u)) (range (l,u))) == [0..rangeSize (l,u)-1] • rangeSize (l,u) == length (range (l,u)) Minimal complete instance: range, index and inRange. Methods
range :: (a, a) -> [a]

The list of values in the subrange deﬁned by a bounding pair.

185

186
index :: (a, a) -> a -> Int

CHAPTER 19. DATA.IX

The position of a subscript in the subrange.
inRange :: (a, a) -> a -> Bool

It is possible to derive an instance of Ix automatically, using a deriving clause on a data declaration. Such derived instance declarations for the class Ix are only possible for enumerations (i.e. datatypes having only nullary constructors) and single-constructor datatypes, whose constituent types are instances of Ix. A Haskell implementation must provide Ix instances for tuples up to at least size 15. For an enumeration, the nullary constructors are assumed to be numbered left-to-right with the indices being 0 to n-1 inclusive. This is the same numbering deﬁned by the Enum class. For example, given the datatype:
data Colour = Red | Orange | Yellow | Green | Blue | Indigo | Violet

The intersperse function takes an element and a list and ‘intersperses’ that element between the elements of the list. For example,
intersperse ’,’ "abcde" == "a,b,c,d,e" intercalate :: [a] -> [[a]] -> [a] intercalate xs xss is equivalent to (concat (intersperse xs xss)). It inserts the list xs in between the lists in xss and concatenates the result. transpose :: [[a]] -> [[a]]

The transpose function transposes the rows and columns of its argument. For example,

foldr1 :: (a -> a -> a) -> [a] -> a foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-

empty lists.

192

CHAPTER 20. DATA.LIST

20.3.1

Special folds

concat :: [[a]] -> [a]

Concatenate a list of lists.
concatMap :: (a -> [b]) -> [a] -> [b]

Map a function over a list and concatenate the results.
and :: [Bool] -> Bool and returns the conjunction of a Boolean list. For the result to be True, the list must be ﬁnite; False, however, results from a False value at a ﬁnite index of a ﬁnite or inﬁnite list.

or :: [Bool] -> Bool or returns the disjunction of a Boolean list. For the result to be False, the list must be ﬁnite; True, however, results from a True value at a ﬁnite index of a ﬁnite or inﬁnite list.

any :: (a -> Bool) -> [a] -> Bool

Applied to a predicate and a list, any determines if any element of the list satisﬁes the predicate.
all :: (a -> Bool) -> [a] -> Bool

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate.
sum :: Num a => [a] -> a

The sum function computes the sum of a ﬁnite list of numbers.
product :: Num a => [a] -> a

The product function computes the product of a ﬁnite list of numbers.
maximum :: Ord a => [a] -> a maximum returns the maximum value from a list, which must be non-empty, ﬁnite, and of an ordered type. It is a special case of maximumBy, which allows the programmer to supply their own comparison

function.
minimum :: Ord a => [a] -> a minimum returns the minimum value from a list, which must be non-empty, ﬁnite, and of an ordered type. It is a special case of minimumBy, which allows the programmer to supply their own comparison

scanr1 :: (a -> a -> a) -> [a] -> [a] scanr1 is a variant of scanr that has no starting value argument.

20.4.2

Accumulating maps

mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])

The mapAccumL function behaves like a combination of map and foldl; it applies a function to each element of a list, passing an accumulating parameter from left to right, and returning a ﬁnal value of this accumulator together with the new list.
mapAccumR :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])

The mapAccumR function behaves like a combination of map and foldr; it applies a function to each element of a list, passing an accumulating parameter from right to left, and returning a ﬁnal value of this accumulator together with the new list.

194
repeat :: a -> [a] repeat x is an inﬁnite list, with x the value of every element. replicate :: Int -> a -> [a]

CHAPTER 20. DATA.LIST

replicate n x is a list of length n with x the value of every element. It is an instance of the more general Data.List.genericReplicate, in which n may be of any integral type. cycle :: [a] -> [a] cycle ties a ﬁnite list into a circular one, or equivalently, the inﬁnite repetition of the original list. It is

the identity on inﬁnite lists.

20.4.4

Unfolding

unfoldr :: (b -> Maybe (a, b)) -> b -> [a]

The unfoldr function is a ‘dual’ to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. The function takes the element and returns Nothing if it is done producing the list or returns Just (a,b), in which case, a is a prepended to the list and b is used as the next element in a recursive call. For example,
iterate f == unfoldr (\x -> Just (x, f x))

It is an instance of the more general Data.List.genericDrop, in which n may be of any integral type.
splitAt :: Int -> [a] -> ([a], [a]) splitAt n xs returns a tuple where ﬁrst element is xs preﬁx of length n and second element is the

span :: (a -> Bool) -> [a] -> ([a], [a]) span, applied to a predicate p and a list xs, returns a tuple where ﬁrst element is longest preﬁx (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

The stripPrefix function drops the given preﬁx from a list. It returns Nothing if the list did not start with the preﬁx given, or Just the list after the preﬁx, if it does.
stripPrefix stripPrefix stripPrefix stripPrefix "foo" "foo" "foo" "foo" "foobar" == Just "bar" "foo" == Just "" "barfoo" == Nothing "barfoobaz" == Nothing

group :: Eq a => [a] -> [[a]]

The group function takes a list and returns a list of lists such that the concatenation of the result is equal to the argument. Moreover, each sublist in the result contains only equal elements. For example,
group "Mississippi" = ["M","i","ss","i","ss","i","pp","i"]

It is a special case of groupBy, which allows the programmer to supply their own equality test.
inits :: [a] -> [[a]]

The find function takes a predicate and a list and returns the ﬁrst element in the list matching the predicate, or Nothing if there is no such element.
filter :: (a -> Bool) -> [a] -> [a] filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate;

i.e.,
filter p xs = [ x | x <- xs, p x]

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CHAPTER 20. DATA.LIST

The partition function takes a predicate a list and returns the pair of lists of elements which do and do not satisfy the predicate, respectively; i.e.,
partition p xs == (filter p xs, filter (not . p) xs)

List index (subscript) operator, starting from 0. It is an instance of the more general Data.List.genericIndex, which takes an index of any integral type.
elemIndex :: Eq a => a -> [a] -> Maybe Int

The elemIndex function returns the index of the ﬁrst element in the given list which is equal (by ==) to the query element, or Nothing if there is no such element.
elemIndices :: Eq a => a -> [a] -> [Int]

The findIndex function takes a predicate and a list and returns the index of the ﬁrst element in the list satisfying the predicate, or Nothing if there is no such element.
findIndices :: (a -> Bool) -> [a] -> [Int]

The findIndices function extends findIndex, by returning the indices of all elements satisfying the predicate, in ascending order.

The zip7 function takes seven lists and returns a list of seven-tuples, analogous to zip.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] zipWith generalises zip by zipping with the function given as the ﬁrst argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

The zipWith7 function takes a function which combines seven elements, as well as seven lists and returns a list of their point-wise combination, analogous to zipWith.
unzip :: [(a, b)] -> ([a], [b]) unzip transforms a list of pairs into a list of ﬁrst components and a list of second components.

O(nˆ2). The nub function removes duplicate elements from a list. In particular, it keeps only the ﬁrst occurrence of each element. (The name nub means ‘essence’.) It is a special case of nubBy, which allows the programmer to supply their own equality test.

It is a special case of deleteBy, which allows the programmer to supply their own equality test.
(\\) :: Eq a => [a] -> [a] -> [a]

The \\ function is list difference ((non-associative). In the result of xs \\ ys, the ﬁrst occurrence of each element of ys in turn (if any) has been removed from xs. Thus
(xs ++ ys) \\ xs == ys.

It is a special case of deleteFirstsBy, which allows the programmer to supply their own equality test.
union :: Eq a => [a] -> [a] -> [a]

The union function returns the list union of the two lists. For example,
"dog" ‘union‘ "cow" == "dogcw"

Duplicates, and elements of the ﬁrst list, are removed from the the second list, but if the ﬁrst list contains duplicates, so will the result. It is a special case of unionBy, which allows the programmer to supply their own equality test.
intersect :: Eq a => [a] -> [a] -> [a]

If the ﬁrst list contains duplicates, so will the result.
[1,2,2,3,4] ‘intersect‘ [6,4,4,2] == [2,2,4]

It is a special case of intersectBy, which allows the programmer to supply their own equality test.

20.9.3

Ordered lists

sort :: Ord a => [a] -> [a]

The sort function implements a stable sorting algorithm. It is a special case of sortBy, which allows the programmer to supply their own comparison function.
insert :: Ord a => a -> [a] -> [a]

The insert function takes an element and a list and inserts the element into the list at the last position where it is still less than or equal to the next element. In particular, if the list is sorted before the call, the result will also be sorted. It is a special case of insertBy, which allows the programmer to supply their own comparison function.

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20.10
20.10.1

Generalized functions
The ”By” operations

By convention, overloaded functions have a non-overloaded counterpart whose name is sufﬁxed with ‘By’.

The deleteFirstsBy function takes a predicate and two lists and returns the ﬁrst list with the ﬁrst occurrence of each element of the second list removed.
unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]

The maximumBy function takes a comparison function and a list and returns the greatest element of the list by the comparison function. The list must be ﬁnite and non-empty.
minimumBy :: (a -> a -> Ordering) -> [a] -> a

The minimumBy function takes a comparison function and a list and returns the least element of the list by the comparison function. The list must be ﬁnite and non-empty.

20.10.2

The ”generic” operations

The preﬁx ‘generic’ indicates an overloaded function that is a generalized version of a Prelude function.
genericLength :: Num i => [b] -> i

The genericLength function is an overloaded version of length. In particular, instead of returning an Int, it returns any type which is an instance of Num. It is, however, less efﬁcient than length.
genericTake :: Integral i => i -> [a] -> [a]

The genericTake function is an overloaded version of take, which accepts any Integral value as the number of elements to take.
genericDrop :: Integral i => i -> [a] -> [a]

The genericDrop function is an overloaded version of drop, which accepts any Integral value as the number of elements to drop.
genericSplitAt :: Integral i => i -> [b] -> ([b], [b])

The genericSplitAt function is an overloaded version of splitAt, which accepts any Integral value as the position at which to split.
genericIndex :: Integral a => [b] -> a -> b

The genericIndex function is an overloaded version of !!, which accepts any Integral value as the index.
genericReplicate :: Integral i => i -> a -> [a]

The genericReplicate function is an overloaded version of replicate, which accepts any Integral value as the number of repetitions to make.

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error. The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Data.Either.Either type.
instance instance instance instance instance instance instance Monad Maybe Functor Maybe MonadPlus Maybe Eq a => Eq (Maybe a) Ord a => Ord (Maybe a) Read a => Read (Maybe a) Show a => Show (Maybe a)

maybe :: b -> (a -> b) -> Maybe a -> b

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result. 205

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isJust :: Maybe a -> Bool

CHAPTER 21. DATA.MAYBE

The isJust function returns True iff its argument is of the form Just _.
isNothing :: Maybe a -> Bool

The isNothing function returns True iff its argument is Nothing.
fromJust :: Maybe a -> a

The fromJust function extracts the element out of a Just and throws an error if its argument is Nothing.
fromMaybe :: a -> Maybe a -> a

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.
listToMaybe :: [a] -> Maybe a

The listToMaybe function returns Nothing on an empty list or Just a where a is the ﬁrst element of the list.
maybeToList :: Maybe a -> [a]

The maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.
catMaybes :: [Maybe a] -> [a]

The catMaybes function takes a list of Maybes and returns a list of all the Just values.
mapMaybe :: (a -> Maybe b) -> [a] -> [b]

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it just Just b, then b is included in the result list.

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.
(%) :: Integral a => a -> a -> Ratio a

Forms the ratio of two integral numbers.
numerator :: Integral a => Ratio a -> a

Extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive. 209

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CHAPTER 22. DATA.RATIO

Extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.
approxRational :: RealFrac a => a -> a -> Rational approxRational, applied to two real fractional numbers x and epsilon, returns the simplest rational number within epsilon of x. A rational number y is said to be simpler than another y’ if

"reduce" is a subsidiary function used only in this module. It normalises a ratio by dividing both numerator and denominator by their greatest common divisor. E.g., 12 ‘reduce‘ 8 == 12 ‘reduce‘ (-8) == = = 3 :% 2 3 :% (-2)

This module provides unsigned integer types of unspeciﬁed width (Word) and ﬁxed widths (Word8, Word16, Word32 and Word64). All arithmetic is performed modulo 2ˆn, where n is the number of bits in the type. For coercing between any two integer types, use fromIntegral. Coercing word types to and from integer types preserves representation, not sign. The rules that hold for Enum instances over a bounded type such as Int (see the section of the Haskell language report dealing with arithmetic sequences) also hold for the Enum instances over the various Word types deﬁned here. Right and left shifts by amounts greater than or equal to the width of the type result in a zero result. This is contrary to the behaviour in C, which is undeﬁned; a common interpretation is to truncate the shift count to the width of the type, for example 1 << 32 == 1 in some C implementations.
data Word

the location where the error occurred the error number optional handle associated with the error optional ﬁlename associated with the error

Construct an IOError based on the given Errno value. The optional information can be used to improve the accuracy of error messages.

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throwErrno :: -> String IO a

CHAPTER 26. FOREIGN.C.ERROR

textual description of the error location

Throw an IOError corresponding to the current value of getErrno.

26.1.3

Guards for IO operations that may fail

throwErrnoIf :: -> -> -> (a -> Bool) String IO a IO a

predicate to apply to the result value of the IO operation textual description of the location the IO operation to be executed

Throw an IOError corresponding to the current value of getErrno if the result value of the IO action meets the given predicate.
throwErrnoIf_ :: (a -> Bool) -> String -> IO a -> IO ()

as throwErrnoIf, but discards the result of the IO action after error handling.
throwErrnoIfRetry :: (a -> Bool) -> String -> IO a -> IO a

as throwErrnoIf, but retry the IO action when it yields the error code eINTR - this amounts to the standard retry loop for interrupted POSIX system calls.
throwErrnoIfRetry_ :: (a -> Bool) -> String -> IO a -> IO ()

as throwErrnoIfRetry, but discards the result.
throwErrnoIfMinus1 :: Num a => String -> IO a -> IO a

Throw an IOError corresponding to the current value of getErrno if the IO action returns a result of -1.
throwErrnoIfMinus1_ :: Num a => String -> IO a -> IO ()

as throwErrnoIfMinus1, but discards the result.
throwErrnoIfMinus1Retry :: Num a => String -> IO a -> IO a

Throw an IOError corresponding to the current value of getErrno if the IO action returns a result of -1, but retries in case of an interrupted operation.
throwErrnoIfMinus1Retry_ :: Num a => String -> IO a -> IO ()

Throw an IOError corresponding to the current value of getErrno if the IO action returns nullPtr, but retry in case of an interrupted operation.
throwErrnoIfRetryMayBlock :: -> -> -> -> (a -> Bool) String IO a IO b IO a

predicate to apply to the result value of the IO operation textual description of the location the IO operation to be executed action to execute before retrying if an immediate retry would block

Utilities for primitive marshalling of C strings. The marshalling converts each Haskell character, representing a Unicode code point, to one or more bytes in a manner that, by default, is determined by the current locale. As a consequence, no guarantees can be made about the relative length of a Haskell string and its corresponding C string, and therefore all the marshalling routines include memory allocation. The translation between Unicode and the encoding of the current locale may be lossy.

27.1

C strings

type CString = Ptr CChar

A C string is a reference to an array of C characters terminated by NUL.
type CStringLen = (Ptr CChar, Int)

A string with explicit length information in bytes instead of a terminating NUL (allowing NUL characters in the middle of the string).

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27.1.1

Using a locale-dependent encoding

Currently these functions are identical to their CAString counterparts; eventually they will use an encoding determined by the current locale.
peekCString :: CString -> IO String

Marshal a Haskell string into a NUL terminated C string. • the Haskell string may not contain any NUL characters • new storage is allocated for the C string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
newCStringLen :: String -> IO CStringLen

Marshal a Haskell string into a C string (ie, character array) with explicit length information. • new storage is allocated for the C string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
withCString :: String -> (CString -> IO a) -> IO a

Marshal a Haskell string into a NUL terminated C string using temporary storage. • the Haskell string may not contain any NUL characters • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.
withCStringLen :: String -> (CStringLen -> IO a) -> IO a

Marshal a Haskell string into a C string (ie, character array) in temporary storage, with explicit length information. • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.
charIsRepresentable :: Char -> IO Bool

Determines whether a character can be accurately encoded in a CString. Unrepresentable characters are converted to ’?’. Currently only Latin-1 characters are representable.

27.1. C STRINGS

231

27.1.2

Using 8-bit characters

These variants of the above functions are for use with C libraries that are ignorant of Unicode. These functions should be used with care, as a loss of information can occur.
castCharToCChar :: Char -> CChar

Convert a Haskell character to a C character. This function is only safe on the ﬁrst 256 characters.
castCCharToChar :: CChar -> Char

Marshal a Haskell string into a NUL terminated C string. • the Haskell string may not contain any NUL characters • new storage is allocated for the C string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
newCAStringLen :: String -> IO CStringLen

Marshal a Haskell string into a C string (ie, character array) with explicit length information. • new storage is allocated for the C string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
withCAString :: String -> (CString -> IO a) -> IO a

Marshal a Haskell string into a NUL terminated C string using temporary storage. • the Haskell string may not contain any NUL characters • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.
withCAStringLen :: String -> (CStringLen -> IO a) -> IO a

Marshal a Haskell string into a C string (ie, character array) in temporary storage, with explicit length information. • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.

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27.2

C wide strings

These variants of the above functions are for use with C libraries that encode Unicode using the C wchar_t type in a system-dependent way. The only encodings supported are • UTF-32 (the C compiler deﬁnes __STDC_ISO_10646__), or • UTF-16 (as used on Windows systems).
type CWString = Ptr CWchar

A C wide string is a reference to an array of C wide characters terminated by NUL.
type CWStringLen = (Ptr CWchar, Int)

A wide character string with explicit length information in CWchars instead of a terminating NUL (allowing NUL characters in the middle of the string).
peekCWString :: CWString -> IO String

Marshal a Haskell string into a NUL terminated C wide string. • the Haskell string may not contain any NUL characters • new storage is allocated for the C wide string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
newCWStringLen :: String -> IO CWStringLen

Marshal a Haskell string into a C wide string (ie, wide character array) with explicit length information. • new storage is allocated for the C wide string and must be explicitly freed using Foreign.Marshal.Alloc.free or Foreign.Marshal.Alloc.finalizerFree.
withCWString :: String -> (CWString -> IO a) -> IO a

Marshal a Haskell string into a NUL terminated C wide string using temporary storage. • the Haskell string may not contain any NUL characters • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.
withCWStringLen :: String -> (CWStringLen -> IO a) -> IO a

Marshal a Haskell string into a NUL terminated C wide string using temporary storage. • the Haskell string may not contain any NUL characters • the memory is freed when the subcomputation terminates (either normally or via an exception), so the pointer to the temporary storage must not be used after this.

These types are needed to accurately represent C function prototypes, in order to access C library interfaces in Haskell. The Haskell system is not required to represent those types exactly as C does, but the following guarantees are provided concerning a Haskell type CT representing a C type t: • If a C function prototype has t as an argument or result type, the use of CT in the corresponding position in a foreign declaration permits the Haskell program to access the full range of values encoded by the C type; and conversely, any Haskell value for CT has a valid representation in C. • sizeOf (undefined :: CT) will yield the same value as sizeof (t) in C. • alignment (undefined :: CT) matches the alignment constraint enforced by the C implementation for t. • The members peek and poke of the Storable class map all values of CT to the corresponding value of t and vice versa. • When an instance of Bounded is deﬁned for CT, the values of minBound and maxBound coincide with t_MIN and t_MAX in C.

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CHAPTER 28. FOREIGN.C.TYPES • When an instance of Eq or Ord is deﬁned for CT, the predicates deﬁned by the type class implement the same relation as the corresponding predicate in C on t. • When an instance of Num, Read, Integral, Fractional, Floating, RealFrac, or RealFloat is deﬁned for CT, the arithmetic operations deﬁned by the type class implement the same function as the corresponding arithmetic operations (if available) in C on t. • When an instance of Bits is deﬁned for CT, the bitwise operation deﬁned by the type class implement the same function as the corresponding bitwise operation in C on t.

28.1.1

Integral types

These types are are represented as newtypes of types in Data.Int and Data.Word, and are instances of Eq, Ord, Num, Read, Show, Enum, Storable, Bounded, Real, Integral and Bits.
data CChar

The type ForeignPtr represents references to objects that are maintained in a foreign language, i.e., that are not part of the data structures usually managed by the Haskell storage manager. The essential difference between ForeignPtrs and vanilla memory references of type Ptr a is that the former may be associated with ﬁnalizers. A ﬁnalizer is a routine that is invoked when the Haskell storage manager detects that - within the Haskell heap and stack - there are no more references left that are pointing to the ForeignPtr. Typically, the ﬁnalizer will, then, invoke routines in the foreign language that free the resources bound by the foreign object. The ForeignPtr is parameterised in the same way as Ptr. The type argument of ForeignPtr should normally be an instance of class Storable.
instance Eq (ForeignPtr a) instance Ord (ForeignPtr a) instance Show (ForeignPtr a) type FinalizerPtr a = FunPtr (Ptr a -> IO ())

A ﬁnalizer is represented as a pointer to a foreign function that, at ﬁnalisation time, gets as an argument a plain pointer variant of the foreign pointer that the ﬁnalizer is associated with. 243

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type FinalizerEnvPtr env a = FunPtr (Ptr env -> Ptr a -> IO ())

29.1.1

Basic operations

newForeignPtr :: FinalizerPtr a -> Ptr a -> IO (ForeignPtr a)

Turns a plain memory reference into a foreign pointer, and associates a ﬁnaliser with the reference. The ﬁnaliser will be executed after the last reference to the foreign object is dropped. There is no guarantee of promptness, however the ﬁnalizer will be executed before the program exits.
newForeignPtr_ :: Ptr a -> IO (ForeignPtr a)

Turns a plain memory reference into a foreign pointer that may be associated with ﬁnalizers by using addForeignPtrFinalizer.
addForeignPtrFinalizer :: FinalizerPtr a -> ForeignPtr a -> IO ()

This function adds a ﬁnalizer to the given foreign object. The ﬁnalizer will run before all other ﬁnalizers for the same object which have already been registered.
newForeignPtrEnv :: FinalizerEnvPtr env a -> Ptr env -> Ptr a -> IO (ForeignPtr a)

This variant of newForeignPtr adds a ﬁnalizer that expects an environment in addition to the ﬁnalized pointer. The environment that will be passed to the ﬁnalizer is ﬁxed by the second argument to newForeignPtrEnv.
addForeignPtrFinalizerEnv :: FinalizerEnvPtr env a -> Ptr env -> ForeignPtr a -> IO ()

Like addForeignPtrFinalizerEnv but allows the ﬁnalizer to be passed an additional environment parameter to be passed to the ﬁnalizer. The environment passed to the ﬁnalizer is ﬁxed by the second argument to addForeignPtrFinalizerEnv
withForeignPtr :: ForeignPtr a -> (Ptr a -> IO b) -> IO b

This is a way to look at the pointer living inside a foreign object. This function takes a function which is applied to that pointer. The resulting IO action is then executed. The foreign object is kept alive at least during the whole action, even if it is not used directly inside. Note that it is not safe to return the pointer from the action and use it after the action completes. All uses of the pointer should be inside the withForeignPtr bracket. The reason for this unsafeness is the same as for unsafeForeignPtrToPtr below: the ﬁnalizer may run earlier than expected, because the compiler can only track usage of the ForeignPtr object, not a Ptr object made from it. This function is normally used for marshalling data to or from the object pointed to by the ForeignPtr, using the operations from the Storable class.

29.1.2

Low-level operations

unsafeForeignPtrToPtr :: ForeignPtr a -> Ptr a

This function extracts the pointer component of a foreign pointer. This is a potentially dangerous

29.1. FINALISED DATA POINTERS

245

operations, as if the argument to unsafeForeignPtrToPtr is the last usage occurrence of the given foreign pointer, then its ﬁnalizer(s) will be run, which potentially invalidates the plain pointer just obtained. Hence, touchForeignPtr must be used wherever it has to be guaranteed that the pointer lives on - i.e., has another usage occurrence. To avoid subtle coding errors, hand written marshalling code should preferably use
Foreign.ForeignPtr.withForeignPtr rather than combinations of unsafeForeignPtrToPtr and touchForeignPtr. However, the latter routines are occasionally preferred in tool generated

marshalling code.
touchForeignPtr :: ForeignPtr a -> IO ()

This function ensures that the foreign object in question is alive at the given place in the sequence of IO actions. In particular withForeignPtr does a touchForeignPtr after it executes the user action. Note that this function should not be used to express dependencies between ﬁnalizers on ForeignPtrs. For example, if the ﬁnalizer for a ForeignPtr F1 calls touchForeignPtr on a second ForeignPtr F2, then the only guarantee is that the ﬁnalizer for F2 is never started before the ﬁnalizer for F1. They might be started together if for example both F1 and F2 are otherwise unreachable. In general, it is not recommended to use ﬁnalizers on separate objects with ordering constraints between them. To express the ordering robustly requires explicit synchronisation between ﬁnalizers.
castForeignPtr :: ForeignPtr a -> ForeignPtr b

This function casts a ForeignPtr parameterised by one type into another type.

29.1.3

Allocating managed memory

mallocForeignPtr :: Storable a => IO (ForeignPtr a)

Allocate some memory and return a ForeignPtr to it. The memory will be released automatically when the ForeignPtr is discarded.
mallocForeignPtr is equivalent to do { p <- malloc; newForeignPtr finalizerFree p }

although it may be implemented differently internally: you may not assume that the memory returned by mallocForeignPtr has been allocated with Foreign.Marshal.Alloc.malloc.
mallocForeignPtrBytes :: Int -> IO (ForeignPtr a)

This function is similar to mallocForeignPtr, except that the size of the memory required is given explicitly as a number of bytes.
mallocForeignPtrArray :: Storable a => Int -> IO (ForeignPtr a)

This function is similar to Foreign.Marshal.Array.mallocArray, but yields a memory area that has a ﬁnalizer attached that releases the memory area. As with mallocForeignPtr, it is not guaranteed that the block of memory was allocated by Foreign.Marshal.Alloc.malloc.
mallocForeignPtrArray0 :: Storable a => Int -> IO (ForeignPtr a)

This function is similar to Foreign.Marshal.Array.mallocArray0, but yields a memory area that has a ﬁnalizer attached that releases the memory area. As with mallocForeignPtr, it is not guaranteed that the block of memory was allocated by Foreign.Marshal.Alloc.malloc.

Sometimes an external entity is a pure function, except that it passes arguments and/or results via pointers. The function unsafeLocalState permits the packaging of such entities as pure functions. The only IO operations allowed in the IO action passed to unsafeLocalState are (a) local allocation (alloca, allocaBytes and derived operations such as withArray and withCString), and (b) pointer operations (Foreign.Storable and Foreign.Ptr) on the pointers to local storage, and (c) foreign functions whose only observable effect is to read and/or write the locally allocated memory. Passing an IO operation that does not obey these rules results in undeﬁned behaviour. It is expected that this operation will be replaced in a future revision of Haskell.

The module Foreign.Marshal.Alloc provides operations to allocate and deallocate blocks of raw memory (i.e., unstructured chunks of memory outside of the area maintained by the Haskell storage manager). These memory blocks are commonly used to pass compound data structures to foreign functions or to provide space in which compound result values are obtained from foreign functions. If any of the allocation functions fails, a value of nullPtr is produced. If free or reallocBytes is applied to a memory area that has been allocated with alloca or allocaBytes, the behaviour is undeﬁned. Any further access to memory areas allocated with alloca or allocaBytes, after the computation that was passed to the allocation function has terminated, leads to undeﬁned behaviour. Any further access to the memory area referenced by a pointer passed to realloc, reallocBytes, or free entails undeﬁned behaviour.

The memory is freed when f terminates (either normally or via an exception), so the pointer passed to f must not be used after this.

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allocaBytes :: Int -> (Ptr a -> IO b) -> IO b allocaBytes n f executes the computation f, passing as argument a pointer to a temporarily allocated block of memory of n bytes. The block of memory is sufﬁciently aligned for any of the basic foreign types that ﬁts into a memory block of the allocated size.

The memory is freed when f terminates (either normally or via an exception), so the pointer passed to f must not be used after this.

31.1.2

Dynamic allocation

malloc :: Storable a => IO (Ptr a)

Allocate a block of memory that is sufﬁcient to hold values of type a. The size of the area allocated is determined by the sizeOf method from the instance of Storable for the appropriate type. The memory may be deallocated using free or finalizerFree when no longer required.
mallocBytes :: Int -> IO (Ptr a)

Allocate a block of memory of the given number of bytes. The block of memory is sufﬁciently aligned for any of the basic foreign types that ﬁts into a memory block of the allocated size. The memory may be deallocated using free or finalizerFree when no longer required.
realloc :: Storable b => Ptr a -> IO (Ptr b)

Resize a memory area that was allocated with malloc or mallocBytes to the size needed to store values of type b. The returned pointer may refer to an entirely different memory area, but will be suitably aligned to hold values of type b. The contents of the referenced memory area will be the same as of the original pointer up to the minimum of the original size and the size of values of type b. If the argument to realloc is nullPtr, realloc behaves like malloc.
reallocBytes :: Ptr a -> Int -> IO (Ptr a)

Resize a memory area that was allocated with malloc or mallocBytes to the given size. The returned pointer may refer to an entirely different memory area, but will be sufﬁciently aligned for any of the basic foreign types that ﬁts into a memory block of the given size. The contents of the referenced memory area will be the same as of the original pointer up to the minimum of the original size and the given size. If the pointer argument to reallocBytes is nullPtr, reallocBytes behaves like malloc. If the requested size is 0, reallocBytes behaves like free.
free :: Ptr a -> IO ()

Free a block of memory that was allocated with malloc, mallocBytes, realloc, reallocBytes, Foreign.Marshal.Utils.new or any of the newX functions in Foreign.Marshal.Array or Foreign.C.String.
finalizerFree :: FinalizerPtr a

A pointer to a foreign function equivalent to free, which may be used as a ﬁnalizer (cf Foreign.ForeignPtr.ForeignPtr) for storage allocated with malloc, mallocBytes, realloc or reallocBytes.

The module Foreign.Marshal.Array provides operations for marshalling Haskell lists into monolithic arrays and vice versa. Most functions come in two ﬂavours: one for arrays terminated by a special termination element and one where an explicit length parameter is used to determine the extent of an array. The typical example for the former case are C’s NUL terminated strings. However, please note that C strings should usually be marshalled using the functions provided by Foreign.C.String as the Unicode encoding has to be taken into account. All functions speciﬁcally operating on arrays that are terminated by a special termination element have a name ending on 0—e.g., mallocArray allocates space for an array of the given size, whereas mallocArray0 allocates space for one more element to ensure that there is room for the terminator.

32.1
32.1.1

Marshalling arrays
Allocation
storage for the given number of elements of a storable type (like

Write a list of storable elements into a newly allocated, consecutive sequence of storable values, where the end is ﬁxed by the given end marker
withArray :: Storable a => [a] -> (Ptr a -> IO b) -> IO b

Temporarily store a list of storable values in memory (like Foreign.Marshal.Utils.with, but for multiple elements).

Copy the given number of elements from the second array (source) into the ﬁrst array (destination); the copied areas may not overlap
moveArray :: Storable a => Ptr a -> Ptr a -> Int -> IO ()

Copy the given number of elements from the second array (source) into the ﬁrst array (destination); the copied areas may overlap

32.1.5

Finding the length

lengthArray0 :: (Storable a, Eq a) => a -> Ptr a -> IO Int

Return the number of elements in an array, excluding the terminator

32.1.6

Indexing

advancePtr :: Storable a => Ptr a -> Int -> Ptr a

Advance a pointer into an array by the given number of elements

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CHAPTER 32. FOREIGN.MARSHAL.ARRAY

Chapter 33

Foreign.Marshal.Error

module Foreign.Marshal.Error ( throwIf, throwIf_, throwIfNeg, ) where

throwIfNeg_,

throwIfNull,

void

throwIf :: -> -> -> (a (a IO IO -> Bool) -> String) a a

error condition on the result of the IO action computes an error message from erroneous results of the IO action the IO action to be executed

Execute an IO action, throwing a userError if the predicate yields True when applied to the result returned by the IO action. If no exception is raised, return the result of the computation.
throwIf_ :: (a -> Bool) -> (a -> String) -> IO a -> IO ()

with :: Storable a => a -> (Ptr a -> IO b) -> IO b with val f executes the computation f, passing as argument a pointer to a temporarily allocated block of memory into which val has been marshalled (the combination of alloca and poke).

The memory is freed when f terminates (either normally or via an exception), so the pointer passed to f must not be used after this.
new :: Storable a => a -> IO (Ptr a)

Allocate a block of memory and marshal a value into it (the combination of malloc and poke). The size of the area allocated is determined by the Foreign.Storable.sizeOf method from the instance of Storable for the appropriate type. The memory may be deallocated using Foreign.Marshal.Alloc.free Foreign.Marshal.Alloc.finalizerFree when no longer required. or

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34.1.2

Marshalling of Boolean values (non-zero corresponds to True)

fromBool :: Num a => Bool -> a

Convert a Haskell Bool to its numeric representation
toBool :: Num a => a -> Bool

The module Foreign.Ptr provides typed pointers to foreign entities. We distinguish two kinds of pointers: pointers to data and pointers to functions. It is understood that these two kinds of pointers may be represented differently as they may be references to data and text segments, respectively.

35.1

Data pointers

data Ptr a

A value of type Ptr a represents a pointer to an object, or an array of objects, which may be marshalled to or from Haskell values of type a. The type a will often be an instance of class Foreign.Storable.Storable which provides the marshalling operations. However this is not essential, and you can provide your own operations to access the pointer. For example you might write small foreign functions to get or set the ﬁelds of a C struct.
instance instance instance instance Eq (Ptr a) Ord (Ptr a) Show (Ptr a) Storable (Ptr a)

nullPtr :: Ptr a

The constant nullPtr contains a distinguished value of Ptr that is not associated with a valid memory location. 259

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castPtr :: Ptr a -> Ptr b

CHAPTER 35. FOREIGN.PTR

The castPtr function casts a pointer from one type to another.
plusPtr :: Ptr a -> Int -> Ptr b

Advances the given address by the given offset in bytes.
alignPtr :: Ptr a -> Int -> Ptr a

Given an arbitrary address and an alignment constraint, alignPtr yields the next higher address that fulﬁlls the alignment constraint. An alignment constraint x is fulﬁlled by any address divisible by x. This operation is idempotent.
minusPtr :: Ptr a -> Ptr b -> Int

Computes the offset required to get from the second to the ﬁrst argument. We have
p2 == p1 ‘plusPtr‘ (p2 ‘minusPtr‘ p1)

35.2

Function pointers

data FunPtr a

A value of type FunPtr a is a pointer to a function callable from foreign code. The type a will normally be a foreign type, a function type with zero or more arguments where • the argument types are marshallable foreign types, i.e. Char, Int, Double, Float, Bool, Data.Int.Int8, Data.Int.Int16, Data.Int.Int32, Data.Int.Int64, Data.Word.Word8, Data.Word.Word16, Data.Word.Word32, Data.Word.Word64, Ptr a, FunPtr a, Foreign.StablePtr.StablePtr a or a renaming of any of these using newtype. • the return type is either a marshallable foreign type or has the form IO t where t is a marshallable foreign type or (). A value of type FunPtr a may be a pointer to a foreign function, either returned by another foreign function or imported with a a static address import like
foreign import ccall "stdlib.h &free" p_free :: FunPtr (Ptr a -> IO ())

Calls to wrapper stubs like mkCompare allocate storage, which should be released with Foreign.Ptr.freeHaskellFunPtr when no longer required. To convert FunPtr values to corresponding Haskell functions, one can deﬁne a dynamic stub for the speciﬁc foreign type, e.g.

The constant nullFunPtr contains a distinguished value of FunPtr that is not associated with a valid memory location.
castFunPtr :: FunPtr a -> FunPtr b

Casts a FunPtr to a FunPtr of a different type.
castFunPtrToPtr :: FunPtr a -> Ptr b

Casts a FunPtr to a Ptr. Note: this is valid only on architectures where data and function pointers range over the same set of addresses, and should only be used for bindings to external libraries whose interface already relies on this assumption.
castPtrToFunPtr :: Ptr a -> FunPtr b

Casts a Ptr to a FunPtr. Note: this is valid only on architectures where data and function pointers range over the same set of addresses, and should only be used for bindings to external libraries whose interface already relies on this assumption.
freeHaskellFunPtr :: FunPtr a -> IO ()

Release the storage associated with the given FunPtr, which must have been obtained from a wrapper stub. This should be called whenever the return value from a foreign import wrapper function is no longer required; otherwise, the storage it uses will leak.

A stable pointer is a reference to a Haskell expression that is guaranteed not to be affected by garbage collection, i.e., it will neither be deallocated nor will the value of the stable pointer itself change during garbage collection (ordinary references may be relocated during garbage collection). Consequently, stable pointers can be passed to foreign code, which can treat it as an opaque reference to a Haskell value. A value of type StablePtr a is a stable pointer to a Haskell expression of type a.
instance Eq (StablePtr a) instance Storable (StablePtr a)

newStablePtr :: a -> IO (StablePtr a)

Create a stable pointer referring to the given Haskell value.
deRefStablePtr :: StablePtr a -> IO a

Obtain the Haskell value referenced by a stable pointer, i.e., the same value that was passed to the corresponding call to makeStablePtr. If the argument to deRefStablePtr has already been freed using freeStablePtr, the behaviour of deRefStablePtr is undeﬁned. 263

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CHAPTER 36. FOREIGN.STABLEPTR

Dissolve the association between the stable pointer and the Haskell value. Afterwards, if the stable pointer is passed to deRefStablePtr or freeStablePtr, the behaviour is undeﬁned. However, the stable pointer may still be passed to castStablePtrToPtr, but the Foreign.Ptr.Ptr () value returned by castStablePtrToPtr, in this case, is undeﬁned (in particular, it may be Foreign.Ptr.nullPtr). Nevertheless, the call to castStablePtrToPtr is guaranteed not to diverge.
castStablePtrToPtr :: StablePtr a -> Ptr ()

Coerce a stable pointer to an address. No guarantees are made about the resulting value, except that the original stable pointer can be recovered by castPtrToStablePtr. In particular, the address may not refer to an accessible memory location and any attempt to pass it to the member functions of the class Foreign.Storable.Storable leads to undeﬁned behaviour.
castPtrToStablePtr :: Ptr () -> StablePtr a

The inverse of castStablePtrToPtr, i.e., we have the identity
sp == castPtrToStablePtr (castStablePtrToPtr sp)

for any stable pointer sp on which freeStablePtr has not been executed yet. Moreover, castPtrToStablePtr may only be applied to pointers that have been produced by castStablePtrToPtr.

36.1.1

The C-side interface

The following deﬁnition is available to C programs inter-operating with Haskell code when including the header HsFFI.h.
typedef void *HsStablePtr;

Note that no assumptions may be made about the values representing stable pointers. In fact, they need not even be valid memory addresses. The only guarantee provided is that if they are passed back to Haskell land, the function deRefStablePtr will be able to reconstruct the Haskell value referred to by the stable pointer.

The member functions of this class facilitate writing values of primitive types to raw memory (which may have been allocated with the above mentioned routines) and reading values from blocks of raw memory. The class, furthermore, includes support for computing the storage requirements and alignment restrictions of storable types. Memory addresses are represented as values of type Ptr a, for some a which is an instance of class Storable. The type argument to Ptr helps provide some valuable type safety in FFI code (you can’t mix pointers of different types without an explicit cast), while helping the Haskell type system ﬁgure out which marshalling method is needed for a given pointer. All marshalling between Haskell and a foreign language ultimately boils down to translating Haskell data structures into the binary representation of a corresponding data structure of the foreign language and vice versa. To code this marshalling in Haskell, it is necessary to manipulate primitive data types stored in unstructured memory blocks. The class Storable facilitates this manipulation on all types for which it is instantiated, which are the standard basic types of Haskell, the ﬁxed size Int types (Int8, Int16, Int32, Int64), the ﬁxed size Word types (Word8, Word16, Word32, Word64), StablePtr, all types from Foreign.C.Types, as well as Ptr. Minimal complete deﬁnition: sizeOf, alignment, one of peek, peekElemOff and peekByteOff, and one of poke, pokeElemOff and pokeByteOff. 265

266 Methods
sizeOf :: a -> Int

CHAPTER 37. FOREIGN.STORABLE

Computes the storage requirements (in bytes) of the argument. The value of the argument is not used.
alignment :: a -> Int

Computes the alignment constraint of the argument. An alignment constraint x is fulﬁlled by any address divisible by x. The value of the argument is not used.
peekElemOff :: Ptr a -> Int -> IO a

Read a value from a memory area regarded as an array of values of the same kind. The ﬁrst argument speciﬁes the start address of the array and the second the index into the array (the ﬁrst element of the array has index 0). The following equality holds,
peekElemOff addr idx = IOExts.fixIO $ \result -> peek (addr ‘plusPtr‘ (idx * sizeOf result))

Note that this is only a speciﬁcation, not necessarily the concrete implementation of the function.
pokeElemOff :: Ptr a -> Int -> a -> IO ()

Write a value to a memory area regarded as an array of values of the same kind. The following equality holds:
pokeElemOff addr idx x = poke (addr ‘plusPtr‘ (idx * sizeOf x)) x peekByteOff :: Ptr b -> Int -> IO a

Write a value to a memory location given by a base address and offset. The following equality holds:
pokeByteOff addr off x = poke (addr ‘plusPtr‘ off) x peek :: Ptr a -> IO a

Read a value from the given memory location. Note that the peek and poke functions might require properly aligned addresses to function correctly. This is architecture dependent; thus, portable code should ensure that when peeking or poking values of some type a, the alignment constraint for a, as given by the function alignment is fulﬁlled.
poke :: Ptr a -> a -> IO ()

Write the given value to the given memory location. Alignment restrictions might apply; see peek.

Show a signed RealFloat value using scientiﬁc (exponential) notation (e.g. 2.45e2, 1.5e-3). In the call showEFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.
showFFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation (e.g. 245000, 0.0015). In the call showFFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.
showGFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientiﬁc notation otherwise. In the call showGFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.
showFloat :: RealFloat a => a -> ShowS

Show a signed RealFloat value to full precision using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientiﬁc notation otherwise.
floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int) floatToDigits takes a base and a non-negative RealFloat number, and returns a list of digits and an exponent. In particular, if x>=0, and floatToDigits base x = ([d1,d2,...,dn], e)

then 1. 2. 3.
n >= 1 x = 0.d1d2...dn * (base**e) 0 <= di <= base-1

38.2

Reading

NB: readInt is the ’dual’ of showIntAtBase, and readDec is the ‘dual’ of showInt. The inconsistent naming is a historical accident.
readSigned :: Real a => ReadS a -> ReadS a

Computation getArgs returns a list of the program’s command line arguments (not including the program name).
getProgName :: IO String

Computation getProgName returns the name of the program as it was invoked. However, this is hard-to-impossible to implement on some non-Unix OSes, so instead, for maximum portability, we just return the leafname of the program as invoked. Even then there are some differences between platforms: on Windows, for example, a program invoked as foo is probably really FOO.EXE, and that is what getProgName will return.
getEnv :: String -> IO String

Computation getEnv var returns the value of the environment variable var. This computation may fail with: • System.IO.Error.isDoesNotExistError if the environment variable does not exist.

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Chapter 40

System.Exit

module System.Exit ( ExitCode(ExitSuccess, ExitFailure), ) where

exitWith,

exitFailure,

exitSuccess

data ExitCode = | ExitSuccess ExitFailure Int

indicates successful termination; indicates program failure with an exit code. The exact interpretation of the code is operating-system dependent. In particular, some values may be prohibited (e.g. 0 on a POSIX-compliant system).

Computation exitWith code terminates the program, returning code to the program’s caller. The caller may interpret the return code as it wishes, but the program should return ExitSuccess to mean normal completion, and ExitFailure n to mean that the program encountered a problem from which it could not recover. The value exitFailure is equal to exitWith (ExitFailure exitfail), where exitfail is implementation-dependent. exitWith bypasses the error handling in the I/O monad and cannot be intercepted by catch from the Prelude.
exitFailure :: IO a

The computation exitFailure is equivalent to exitWith (ExitFailure exitfail), where exitfail is implementation-dependent. 275

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exitSuccess :: IO a

CHAPTER 40. SYSTEM.EXIT

The computation exitSuccess is equivalent to exitWith ExitSuccess, It terminates the program successfully.

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a. There is really only one way to ”perform” an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn’t possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.
IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class. instance Monad IO instance Functor IO

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fixIO :: (a -> IO a) -> IO a

CHAPTER 41. SYSTEM.IO

41.2

Files and handles

type FilePath = String

File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that ﬁle.
data Handle

Haskell deﬁnes operations to read and write characters from and to ﬁles, represented by values of type Handle. Each value of this type is a handle: a record used by the Haskell run-time system to manage I/O with ﬁle system objects. A handle has at least the following properties: • whether it manages input or output or both; • whether it is open, closed or semi-closed; • whether the object is seekable; • whether buffering is disabled, or enabled on a line or block basis; • a buffer (whose length may be zero). Most handles will also have a current I/O position indicating where the next input or output operation will occur. A handle is readable if it manages only input or both input and output; likewise, it is writable if it manages only output or both input and output. A handle is open when ﬁrst allocated. Once it is closed it can no longer be used for either input or output, though an implementation cannot re-use its storage while references remain to it. Handles are in the Show and Eq classes. The string produced by showing a handle is system dependent; it should include enough information to identify the handle for debugging. A handle is equal according to == only to itself; no attempt is made to compare the internal state of different handles for equality.
instance Eq Handle instance Show Handle

41.2.1

Standard handles

Three handles are allocated during program initialisation, and are initially open.
stdin :: Handle

Computation openFile file mode allocates and returns a new, open handle to manage the ﬁle file. It manages input if mode is ReadMode, output if mode is WriteMode or AppendMode, and both input and output if mode is ReadWriteMode. If the ﬁle does not exist and it is opened for output, it should be created as a new ﬁle. If mode is WriteMode and the ﬁle already exists, then it should be truncated to zero length. Some operating systems delete empty ﬁles, so there is no guarantee that the ﬁle will exist following an openFile with mode WriteMode unless it is subsequently written to successfully. The handle is positioned at the end of the ﬁle if mode is AppendMode, and otherwise at the beginning (in which case its internal position is 0). The initial buffer mode is implementation-dependent. This operation may fail with: • isAlreadyInUseError if the ﬁle is already open and cannot be reopened; • isDoesNotExistError if the ﬁle does not exist; or • isPermissionError if the user does not have permission to open the ﬁle.
data IOMode = | | | ReadMode WriteMode AppendMode ReadWriteMode

Computation hClose hdl makes handle hdl closed. Before the computation ﬁnishes, if hdl is writable its buffer is ﬂushed as for hFlush. Performing hClose on a handle that has already been closed has no effect; doing so is not an error. All other operations on a closed handle will fail. If hClose fails for any reason, any further operations (apart from hClose) on the handle will still fail as if hdl had been successfully closed.

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41.3.3

Special cases

These functions are also exported by the Prelude.
readFile :: FilePath -> IO String

The readFile function reads a ﬁle and returns the contents of the ﬁle as a string. The ﬁle is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO ()

The computation appendFile file str function appends the string str, to the ﬁle file. Note that writeFile and appendFile write a literal string to a ﬁle. To write a value of any printable type, as with print, use the show function to convert the value to a string ﬁrst.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

41.3.4

File locking

Implementations should enforce as far as possible, at least locally to the Haskell process, multiple-reader single-writer locking on ﬁles. That is, there may either be many handles on the same ﬁle which manage input, or just one handle on the ﬁle which manages output. If any open or semi-closed handle is managing a ﬁle for output, no new handle can be allocated for that ﬁle. If any open or semi-closed handle is managing a ﬁle for input, new handles can only be allocated if they do not manage output. Whether two ﬁles are the same is implementation-dependent, but they should normally be the same if they have the same absolute path name and neither has been renamed, for example. Warning: the readFile operation holds a semi-closed handle on the ﬁle until the entire contents of the ﬁle have been consumed. It follows that an attempt to write to a ﬁle (using writeFile, for example) that was earlier opened by readFile will usually result in failure with System.IO.Error.isAlreadyInUseError.

For a readable handle hdl, hIsEOF hdl returns True if no further input can be taken from hdl or for a physical ﬁle, if the current I/O position is equal to the length of the ﬁle. Otherwise, it returns False. NOTE: hIsEOF may block, because it has to attempt to read from the stream to determine whether there is any more data to be read.
isEOF :: IO Bool

The computation isEOF is identical to hIsEOF, except that it works only on stdin.

buffering is disabled if possible. line-buffering should be enabled if possible. block-buffering should be enabled if possible. The size of the buffer is n items if the argument is Just n and is otherwise implementation-dependent.

Three kinds of buffering are supported: line-buffering, block-buffering or no-buffering. These modes have the following effects. For output, items are written out, or ﬂushed, from the internal buffer according to the buffer mode: • line-buffering: the entire output buffer is ﬂushed whenever a newline is output, the buffer overﬂows, a System.IO.hFlush is issued, or the handle is closed. • block-buffering: the entire buffer is written out whenever it overﬂows, a System.IO.hFlush is issued, or the handle is closed. • no-buffering: output is written immediately, and never stored in the buffer. An implementation is free to ﬂush the buffer more frequently, but not less frequently, than speciﬁed above. The output buffer is emptied as soon as it has been written out. Similarly, input occurs according to the buffer mode for the handle: • line-buffering: when the buffer for the handle is not empty, the next item is obtained from the buffer; otherwise, when the buffer is empty, characters up to and including the next newline character are read into the buffer. No characters are available until the newline character is available or the buffer is full. • block-buffering: when the buffer for the handle becomes empty, the next block of data is read into the buffer. • no-buffering: the next input item is read and returned. The System.IO.hLookAhead operation implies that even a no-buffered handle may require a one-character buffer. The default buffering mode when a handle is opened is implementation-dependent and may depend on the ﬁle system object which is attached to that handle. For most implementations, physical ﬁles will normally be block-buffered and terminals will normally be line-buffered.

Computation hSetBuffering hdl mode sets the mode of buffering for handle hdl on subsequent reads and writes. If the buffer mode is changed from BlockBuffering or LineBuffering to NoBuffering, then • if hdl is writable, the buffer is ﬂushed as for hFlush; • if hdl is not writable, the contents of the buffer is discarded. This operation may fail with: • isPermissionError if the handle has already been used for reading or writing and the implementation does not allow the buffering mode to be changed.
hGetBuffering :: Handle -> IO BufferMode

The action hFlush hdl causes any items buffered for output in handle hdl to be sent immediately to the operating system. This operation may fail with: • isFullError if the device is full; • isPermissionError if a system resource limit would be exceeded. It is unspeciﬁed whether the characters in the buffer are discarded or retained under these circumstances.

41.4.4

Repositioning handles

hGetPosn :: Handle -> IO HandlePosn

Computation hGetPosn hdl returns the current I/O position of hdl as a value of the abstract type HandlePosn.
hSetPosn :: HandlePosn -> IO ()

If a call to hGetPosn hdl returns a position p, then computation hSetPosn p sets the position of hdl to the position it held at the time of the call to hGetPosn. This operation may fail with: • isPermissionError if a system resource limit would be exceeded.
data HandlePosn

Computation hSeek hdl mode i sets the position of handle hdl depending on mode. The offset i is given in terms of 8-bit bytes. If hdl is block- or line-buffered, then seeking to a position which is not in the current buffer will ﬁrst cause any items in the output buffer to be written to the device, and then cause the input buffer to be discarded. Some handles may not be seekable (see hIsSeekable), or only support a subset of the possible positioning operations (for instance, it may only be possible to seek to the end of a tape, or to a positive offset from the beginning or current position). It is not possible to set a negative I/O position, or for a physical ﬁle, an I/O position beyond the current end-of-ﬁle. This operation may fail with: • isIllegalOperationError if the Handle is not seekable, or does not support the requested seek mode. * isPermissionError if a system resource limit would be exceeded.
data SeekMode

the position of hdl is set to i. the position of hdl is set to offset i from the current position. the position of hdl is set to offset i from the end of the ﬁle. A mode that determines the effect of hSeek hdl mode i.
= | | AbsoluteSeek RelativeSeek SeekFromEnd instance instance instance instance instance instance Enum SeekMode Eq SeekMode Ord SeekMode Read SeekMode Show SeekMode Ix SeekMode

hTell :: Handle -> IO Integer

Computation hTell hdl returns the current position of the handle hdl, as the number of bytes from the beginning of the ﬁle. The value returned may be subsequently passed to hSeek to reposition the handle to the current position. This operation may fail with: • isIllegalOperationError if the Handle is not seekable.

Set the echoing status of a handle connected to a terminal.
hGetEcho :: Handle -> IO Bool

Get the echoing status of a handle connected to a terminal.

41.4.7

Showing handle state

hShow :: Handle -> IO String hShow is in the IO monad, and gives more comprehensive output than the (pure) instance of Show for Handle.

41.5
41.5.1

Text input and output
Text input

hWaitForInput :: Handle -> Int -> IO Bool

Computation hWaitForInput hdl t waits until input is available on handle hdl. It returns True as soon as input is available on hdl, or False if no input is available within t milliseconds. Note that hWaitForInput waits until one or more full characters are available, which means that it needs to do decoding, and hence may fail with a decoding error. If t is less than zero, then hWaitForInput waits indeﬁnitely. This operation may fail with: • isEOFError if the end of ﬁle has been reached. • a decoding error, if the input begins with an invalid byte sequence in this Handle’s encoding.
hReady :: Handle -> IO Bool

Computation hReady hdl indicates whether at least one item is available for input from handle hdl. This operation may fail with: • System.IO.Error.isEOFError if the end of ﬁle has been reached.
hGetChar :: Handle -> IO Char

Computation hGetChar hdl reads a character from the ﬁle or channel managed by hdl, blocking until a character is available. This operation may fail with:

41.5. TEXT INPUT AND OUTPUT • isEOFError if the end of ﬁle has been reached.
hGetLine :: Handle -> IO String

285

Computation hGetLine hdl reads a line from the ﬁle or channel managed by hdl. This operation may fail with: • isEOFError if the end of ﬁle is encountered when reading the ﬁrst character of the line. If hGetLine encounters end-of-ﬁle at any other point while reading in a line, it is treated as a line terminator and the (partial) line is returned.
hLookAhead :: Handle -> IO Char

Computation hLookAhead returns the next character from the handle without removing it from the input buffer, blocking until a character is available. This operation may fail with: • isEOFError if the end of ﬁle has been reached.
hGetContents :: Handle -> IO String

Computation hGetContents hdl returns the list of characters corresponding to the unread portion of the channel or ﬁle managed by hdl, which is put into an intermediate state, semi-closed. In this state, hdl is effectively closed, but items are read from hdl on demand and accumulated in a special list returned by hGetContents hdl. Any operation that fails because a handle is closed, also fails if a handle is semi-closed. The only exception is hClose. A semi-closed handle becomes closed: • if hClose is applied to it; • if an I/O error occurs when reading an item from the handle; • or once the entire contents of the handle has been read. Once a semi-closed handle becomes closed, the contents of the associated list becomes ﬁxed. The contents of this ﬁnal list is only partially speciﬁed: it will contain at least all the items of the stream that were evaluated prior to the handle becoming closed. Any I/O errors encountered while a handle is semi-closed are simply discarded. This operation may fail with: • isEOFError if the end of ﬁle has been reached.

41.5.2

Text output

hPutChar :: Handle -> Char -> IO ()

Computation hPutChar hdl ch writes the character ch to the ﬁle or channel managed by hdl. Characters may be buffered if buffering is enabled for hdl. This operation may fail with: • isFullError if the device is full; or

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CHAPTER 41. SYSTEM.IO • isPermissionError if another system resource limit would be exceeded.

hPutStr :: Handle -> String -> IO ()

Computation hPutStr hdl s writes the string s to the ﬁle or channel managed by hdl. This operation may fail with: • isFullError if the device is full; or • isPermissionError if another system resource limit would be exceeded.
hPutStrLn :: Handle -> String -> IO ()

The same as hPutStr, but adds a newline character.
hPrint :: Show a => Handle -> a -> IO ()

Computation hPrint hdl t writes the string representation of t given by the shows function to the ﬁle or channel managed by hdl and appends a newline. This operation may fail with: • System.IO.Error.isFullError if the device is full; or • System.IO.Error.isPermissionError if another system resource limit would be exceeded.

41.5.3

Special cases for standard input and output

These functions are also exported by the Prelude.
interact :: (String -> String) -> IO ()

The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.
putChar :: Char -> IO ()

The same as putStr, but adds a newline character.
print :: Show a => a -> IO ()

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline. For example, a program to print the ﬁrst 20 integers and their powers of 2 could be written as:

41.5. TEXT INPUT AND OUTPUT
main = print ([(n, 2ˆn) | n <- [0..19]])

287

getChar :: IO Char

Read a character from the standard input device (same as hGetChar stdin).
getLine :: IO String

Read a line from the standard input device (same as hGetLine stdin).
getContents :: IO String

The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).
readIO :: Read a => String -> IO a

The readIO function is similar to read except that it signals parse failure to the IO monad instead of terminating the program.
readLn :: Read a => IO a

Errors of type IOError are used by the IO monad. This is an abstract type; the module System.IO.Error provides functions to interrogate and construct values of type IOError.
userError :: String -> IOError

Construct an IOError of the given type where the second argument describes the error location and the third and fourth argument contain the ﬁle handle and ﬁle path of the ﬁle involved in the error if applicable. 289

Adds a location description and maybe a ﬁle path and ﬁle handle to an IOError. If any of the ﬁle handle or ﬁle path is not given the corresponding value in the IOError remains unaltered.

42.1.1

Classifying I/O errors

isAlreadyExistsError :: IOError -> Bool

An error indicating that an IO operation failed because one of its arguments already exists.
isDoesNotExistError :: IOError -> Bool

An error indicating that an IO operation failed because one of its arguments does not exist.
isAlreadyInUseError :: IOError -> Bool

An error indicating that an IO operation failed because one of its arguments is a single-use resource, which is already being used (for example, opening the same ﬁle twice for writing might give this error).
isFullError :: IOError -> Bool

An error indicating that an IO operation failed because the device is full.
isEOFError :: IOError -> Bool

An error indicating that an IO operation failed because the end of ﬁle has been reached.
isIllegalOperation :: IOError -> Bool

An error indicating that an IO operation failed because the operation was not possible. Any computation which returns an IO result may fail with isIllegalOperation. In some cases, an implementation will not be able to distinguish between the possible error causes. In this case it should fail with isIllegalOperation.
isPermissionError :: IOError -> Bool

An error indicating that an IO operation failed because the user does not have sufﬁcient operating system privilege to perform that operation.
isUserError :: IOError -> Bool

An abstract type that contains a value for each variant of IOError.
instance Eq IOErrorType instance Show IOErrorType

alreadyExistsErrorType :: IOErrorType

I/O error where the operation failed because one of its arguments already exists.
doesNotExistErrorType :: IOErrorType

I/O error where the operation failed because one of its arguments does not exist.
alreadyInUseErrorType :: IOErrorType

I/O error where the operation failed because one of its arguments is a single-use resource, which is already being used.
fullErrorType :: IOErrorType

I/O error where the operation failed because the device is full.
eofErrorType :: IOErrorType

I/O error where the operation failed because the end of ﬁle has been reached.
illegalOperationErrorType :: IOErrorType

I/O error where the operation is not possible.
permissionErrorType :: IOErrorType

I/O error where the operation failed because the user does not have sufﬁcient operating system privilege to perform that operation.
userErrorType :: IOErrorType

I/O error that is programmer-deﬁned.

42.3

Throwing and catching I/O errors

ioError :: IOError -> IO a

Raise an IOError in the IO monad.

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catch :: IO a -> (IOError -> IO a) -> IO a

CHAPTER 42. SYSTEM.IO.ERROR

The catch function establishes a handler that receives any IOError raised in the action protected by catch. An IOError is caught by the most recent handler established by catch. These handlers are not selective: all IOErrors are caught. Exception propagation must be explicitly provided in a handler by re-raising any unwanted exceptions. For example, in
f = catch g (\e -> if IO.isEOFError e then return [] else ioError e)

the function f returns [] when an end-of-ﬁle exception (cf. isEOFError) occurs in g; otherwise, the exception is propagated to the next outer handler. When an exception propagates outside the main program, the Haskell system prints the associated IOError value and exits the program.
try :: IO a -> IO (Either IOError a)

The construct try comp exposes IO errors which occur within a computation, and which are not fully handled.